Modeling with Linear Equations

\(\begin{aligned}
&\text{A bus is traveling at a constant speed along a straight portion of road. The equation }\\
&d=30t\text{ gives the distance }d,\text{in feet from a road marker, that the bus will be }t \text{ seconds}\\
&\text{after passing the marker. How many feet from the marker will the bus be 2 seconds}\\
&\text{after passing the marker?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=45x+600\\
&\text{The function }f\text{ gives the monthly fee }f(x)\text{, in dollars, a facility charges to keep }x\text{ crates in }\\
&\text{storage. What is the monthly fee, in dollars, the facility charges to keep 50 crates in storage ?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=14+4x\\
&\text{The function }f\text{ represents the total cost, in dollars, of attending an arcade when }x\text{ games }\\&\text{are played. How many games can be played for a total cost of \$58?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=7x+1\\
&\text{The function gives the total number of people on a company retreat with }x\text{ managers.}\\
&\text{What is the total number of people on a company retreat with 7 managers?}\end{aligned}\)

\(\begin{aligned}
&\text{The function }f(x)=-40x+280\text{ gives the predicted height above the ground }f(x)\text{, in feet,}\\
&\mathrm{of~a~model~airplane~}x\text{ minutes after it begins to descend. What is the predicted height}\\
&\text{above the ground, in feet, of the model airplane 4 minutes after it begins to descend?}\\&\end{aligned}\)

\(\begin{aligned}
&\text{The total cost }f(x)\text{, in dollars, to lease a car for 36 months from a particular car dealership is}\\
&\text{given by }f(x)=36x+1,000\text{, where }x\text{ is the monthly payment, in dollars. What is the total}\\
&\text{cost to lease a car when the monthly payment is \$400?}\end{aligned}\)

\(\begin{aligned}
&\text{The function }f(x)=180(x-2)\text{ gives the sum of the interior angles, in degrees, for a}\\
&\text{polygon with }x\text{ sides. What is the sum of the interior angles, in degrees, for a polygon}\\&\text{with 14 sides?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s=40+3t\\
&\text{The equation gives the speed }s\text{, in miles per hour, of a certain car }t\text{ seconds after it began }\\&\text{to accelerate. What is the speed, in miles per hour, of the car 5 seconds after it began to}\\&\text{accelerate?}\end{aligned}\)

\(\begin{aligned}
&\text{The equation }d=33w+100\text{ gives the total amount of money }d\text{, in dollars, that James plans}\\
&\text{to save }w\text{ weeks after he start to save. What is the total amount of money, in dollars, he plans}\\
&\text{to save in 10 weeks?}\end{aligned}\)

\(\begin{aligned}
&\text{A student council group is selling school posters for a fundraiser. They use the function }p(x)=5x-220\\
&\text{to determine their profit }p(x)\text{, in dollars, for selling }x\text{ school posters. In order to earn a profit of \$900,}\\
&\text{how many school posters must they sell?}\end{aligned}\)

\(\begin{aligned}
&\text{The equation }h=\frac{9(v-273.15)}{5}+32\text{ gives the corresponding temperature }h\text{, in degrees Fahrenheit,}\\
&\text{of any substance that has temperature of }v\text{ kelvins, where }v\geq0.\text{ If a substance has a temperature of}\\
&467.33\text{ degrees Fahrenheit, what is the corresponding temperature, in kelvins, of this substance?}
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2.5b+5r=80\\
&\text{The given equation describes the relationship between the number of birds, }b\text{, and the number of}\\
&\mathrm{reptiles,~}r,\text{that can be cared for at a pet care business on a given day. If the business cares for 16 }\\
&\text{reptiles on a given day, how many birds can it care for on this day?}\end{aligned}\)

\(\begin{aligned}
&\text{The equation }x+y=1,440\text{ represents the number of minutes of daylight (between sunrise }\\
&\text{and sunset), }x\text{, and the number of minutes of non-daylight, }y\text{, on a particular day on Oak }\\
&\text{Park, Illinois. If this day has 670 minutes of daylight, how many minutes of non-daylight }\\
&\text{does it have?}\end{aligned}
\)

\(\begin{aligned}
&\text{In 6 days, a polar bear ate 25.8 pounds of fat. Which equation describes the amount of fat, }y,\\
&\text{in pounds, the poar bear ate in these days?}\end{aligned}\)

\(\begin{aligned}
&\text{For a training program, Juan rides his bike at an average rate of 5.7 minutes per mile. Which}\\
&\text{function }m\text{ models the number of minutes it will take Juan to ride }x\text{ miles at this rate?}
\end{aligned}\)

\(\begin{aligned}&\text{A large square has an area of 36 square centimeters}\left(\text{cm}^{2}\right).\text{ Small squares of area }\\
&4\text { cm}^2\text{ are cut out of the large square one by one. Which function }f\text{ gives the area of the}\\
&\text{the resulting figure, in }\text {cm}^2,\mathrm{~after~}x\text{ small squares are cut out?}\end{aligned}\)

\(\begin{aligned}
&\text{A veterinarian recommends that each day a certain rabbit should eat 25 calories per pound of the }\\
&\text{rabbit weight, plus an additional 11 calories. Which equation represents this situation, where }c\\
&\text{is the total number of calories the veterinarian recommends the rabbit should eat each day if the}\\
&\text{rabbit’s weight is }x\text{ pounds?}\end{aligned}\)

\(\begin{aligned}
&\text{Demarcus has 200 Japenese yen (JPY). He needs to exchange Hong Kong dollars (HKD)}\\
&\text{for more JPY. The exchange rate is 14 JPY for every HKD. Which function }f\text{ gives the}\\
&\text{total amount, in JPY, Demarcus will have after exchanging }x\text{ HKD?}\end{aligned}\)

\(\begin{aligned}
&\text{Sean rents a tent at a cost of \$11 per day plus a onetime insurance fee of \$10. Which}\\
&\text{equation represents the total cost, }c\text{, in dollars, to rent the tent with insurance }d\text{ days?}\end{aligned}\)

\(\begin{aligned}
&\text{The linear function }f\text{ gives a company’s profit, in dollars, for selling }x\text{ items. The company’s }\\
&\text{profit is \$190 when it sells 4 items, and its profit is \$670 when it sells 10 items. Which }\\&\text{equation defines }f?\end{aligned}\)

\(\begin{aligned}
&\text{A book-of-the-month club charges \$13 for the first book purchased during the month and an}\\
&\text{additional \$11 for each book after the first. Which equation describes this situation, where }y\\
&\text{is the total cost, in dollars, for books purchased during a month, }x\text{ is the number of books }\\
&\text{purchased during the month,~and~}x>0?\end{aligned}\)

\(\begin{aligned}
&\text{A cooking school is offering a promotion where the first class is free, the second class is half}\\&\text{off the regular price, and the remaining classes are regularly priced. If the regular price of a}\\&\text{class is \$22.80, which function }f\text{ gives the total cost, in dollars, of }x\text{ classes taken using this}\\&\text{promotion, where }x\geq2?\end{aligned}\)

\(\begin{aligned}
&\text{The cost of renting a carpet cleaner is \$52 for the first day and \$26 for each additional day. }\\
&\text{Which of the following functions gives the cost }C(d),\text{in dollars, of renting the cleaner for }d\\
&\text{days, where }d\text{ is a positive integer?}\end{aligned}\)

\(\begin{aligned}
&\text{A window repair specialist charges \$220 for the first two hours of repair plus an hourly fee for each}\\
&\text{additional hour. The total cost for 5 hours of repair \$400. Which function }f\text{ gives the total cost, in}\\
&\text{dollars, for }x\text{ hours of repair, where }x\geq2?\end{aligned}\)

\(\begin{aligned}
&\text{For groups of 25 or more people, a museum charges \$22 per person for the first 25 people}\\
&\text{and \$14 for each additional person. Which function }f\text{ gives the total charge, in dollars,}\\
&\mathrm{for~a~tour~group~with~}n\mathrm{~people,where~}n\geq25?\end{aligned}\)

\(\begin{aligned}
&\text{A polygonal chain is a connected series of line segments whose length is defined as the sum}\\
&\text{of the lengths of the line segments it is made of. A polygonal chain with a length of}\\
&33\text{ centimeters (cm) is extended by adding line segments that each have a length of}\\
&8-r\text{ cm. Which function }f\text{ represents the total length, in cm, of the extended polygonal}\\
&\text{chain after }x\text{ line segments are added?}\end{aligned}\)

\(\begin{aligned}
&\text{A business consultant charges \$444 for the first hour and \$222 for each additional hour of work.}\\
&\text{Which of the following functions gives the charges }C(h),\text{in dollars, for }h\text{ hours of work, where}\\
&h\mathrm{~is~a~positive~integer?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{A plumbing company charges its customers \$112 for the first hour of a plumbing service call}\\
&\text{and \$40 for each additional hour, plus the cost of plumbing parts. Which equation represents}\\
&\text{the total cost }y\text{, in dollars, for an }x\text{-hour plumbing service call where the cost of parts was }\\
&z\mathrm{~and~}x\geq1?\end{aligned}\)

\(\begin{aligned}
&\text{The cost of renting a piece of equipment is \$64}n\text{ for the first day and \$32}n\text{ for each additional }\\
&\text{day, where }n\text{ is a positive integer.Which of the following functions gives the cost }C(x)\text{ in }\\
&\text{dollars, of renting this equipment for }x\text{ days, where }x\text{ is a positive integer?}\end{aligned}\)

\(\begin{aligned}
&\text{A partially filled container containing 24 milliliters of water is placed under a leaky faucet}\\
&\text{that produces one 0.03 milliliter drop of water every 3 seconds. Until the container is full,}\\
&\text{which of the following can be used to represent the volume }v,\text{ in milliliters, of water in the}\\
&\text{container }t\text{ seconds after it is placed under the faucet, where }t\text{ is a multiple of 3?}\end{aligned}\)

\(\begin{aligned}
&\text{A set designer is hammering nails along the top edge of a wall with a length of 3}x\mathrm{~feet,}\\&\mathrm{where~}x\text{ is an integer, that will be used to hang garland. The designer hammers the first nail}\\&\text{at the left edge of the wall. The designer then hammers an additional nail every }\frac{3}{8}\mathrm{~feet~along}\\&\text{the entire length of the wall, starting from the first nail and with the last nail being}\\&\text{hammered at the right edge of the wall. Which equation best represents this situation, where}\\&y\text{ is the number of nails the designer hammers along the entire length of the wall?}\end{aligned}\)

\(\begin{aligned}&\text{During a specific 2-hour period of the day, the mean photosynthetic rate, }P(x),\text{ of a plant}\\&\text{species increases at a constant rate in terms of the photochemical energy available, }x.\\&\text{During this period, }P(300)=9.8,\text{ and the mean photosynthetic rate increases by }0.13\\&\text{micromoles per meter squared per second }(\mu\mathrm{mol}\cdot\mathrm{m}^{-2}\mathrm{s}^{-1})\text{when the photochemical}\\&\text{energy available increases by 5 }\mu\mathrm{mol}\cdot\mathrm{m}^{-2}\mathrm{s}^{-1}.\text{ Which equation gives the mean}\\&\mathrm{photosynthetic~rate,~in~\mu mol\cdot m^{-2}s^{-1},~in~terms~of~the~photochemical~energy~avaliable,}\\&\mathrm{in~\mu mol}\cdot\mathrm{m}^{-2}\mathbf{s}^{-1},\text{ during this period}?\end{aligned}\)

\(\begin{aligned}&\text{A beekeeper’s initial observation of the population of a certain bee colony was 1,600 bees.}\\&\text{The beekeeper set a goal to increase the population to 2,975 bees. The beekeeper uses a}\\&\text{model that predicts the population of this bee colony begins at 1,600 and increases by 110}\\&\text{bees per week in the first two weeks after the initial observation, and then increases by 165}\\&\text{bees per week until the beekeeper’s goal is reached. According to this model, at the end of}\\&\mathrm{week~}w\text{ after the initial observation, where }w > 2,\text{which of the following functions gives the}\\&\text{predicted number of bees still needed to reach the beekeeper’s goal?}\end{aligned}\)

\(\begin{aligned}
&\text{Hassan put up wire fencing along each edge of a rectangular garden with a length of }x\\
&\text{feet and a width of }y\text{ feet. Hassan put up a total of 44 feet of wire fencing. Which}\\
&\text{equation represents this situation?}\end{aligned}\)

\(\begin{aligned}
&\text{A gardner buys two kinds of fertilizer. Fertilizer A contains }\%60\text{ filler materials by weight }\\
&\text{and Fertilizer B contains }\%40\text{ filler materials by weight. Together, the fertilizers bought by }\\
&\text{the gardner contain a total of 240 pounds of filler materials. Which equation models this }\\
&\text{relationship, where }x\text{ is the number of pounds of Fertilizer A and }y\text{ is the number of pounds}\\&\text{of Fertilizer B?}\end{aligned}\)

\(\begin{aligned}
&\text{A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth}\\
&\text{1 point and questions worth 3 points. Which equation represents this situation, where }x\text{ represents}\\
&\text{the number of 1-point questions and }y\text{ represents the number of 3-point questions?}\end{aligned}\)

\(\begin{aligned}
&\text{Casey is raising }h\text{ horses and }g\text{ goats. Each horse requires 2 acres of land, and each }\\
&\text{goat requires 1 acre of land. The }h \text{ horses and }g\text{ goats require 21 acres of land. Which}\\&\text{equation represents this situation?}\end{aligned}\)

\(\begin{aligned}
&\text{A total of 6 squares each have side length }r.\text{ A total of 3 equilateral triangles each have side} \\
&\text{length }t\text{. None of these squares and triangles shares a side. The sum of the perimeters of all }\\
&\text{these squares and triangles is 75. Which equation represents this situation?}\end{aligned}\)

\(\begin{aligned}
&\text{Jay walks at a speed of 3 miles per hour and runs at a speed of 5 miles per hour. He walks for }w\\
&\text{hours and runs for }r\text{ hours for a combined total of 14 miles. Which equation represents this }\\&\text{situation?}\end{aligned}\)

\(\begin{aligned}&\text{A group of students purchase ice cream cones and ice cream sundaes. The cones cost \$1.40}\\&\text{each, and the cost for 19 sundaes is \$64.60. The total cost for the cones and sundaes is}\\&\$85.60.\text{ Which equation represents this situation, where }x\text{ is the number of cones purchased}\\&\mathrm{and~}y\text{ is the number of sundaes purchased?}\end{aligned}\)

\(\begin{aligned}
&\text{Each 3.0-ounce serving of cheddar cheese and each 1.2-ounce serving of tuna provides about 1}\\&\text{microgram of vitamin B12. If a total of 3.1 micrograms of vitamin B12 are consumed from eating }x\\&\text{ounces of cheese and }y\text{ ounces of tuna, which equation best represents this situation?}\end{aligned}\)

\(\begin{aligned}&\text{A city has an area of }x\text{ square miles and a population density of }1,035\text{ people per square mile.}\\&\text{The suburb adjacent to the city has an area of }y\text{ square miles and a population density of }535\\&\text{people per square mile. The combined population of the city and the suburb adjacent to the city}\\&\text{is 13,165 people. Which equation represents this situation?}\end{aligned}\)

\(\begin{aligned}
&\text{The graph represents the total charge, in dollars, by an electrician for }x\text{ hours of work. The }\\
&\text{electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the }\\
&\text{slope of the graph?}\end{aligned}\)

\(\begin{aligned}
&\text{Two students are playing a game. In the first round, Player 1 answers 33 questions. If an}\\
&\text{answer is correct, Player 1 earns 1 point. If an answer is incorrect. Player 2 will earn 1 point}\\
&\text{instead. The graph shows }y=f(x)\mathrm{, where~}y\text{ is the number of points Player 2 will earn when}\\&x\text{ is the number of points Player 1 earns. Which of the following is the best interpretation of}\\&\text{the point }(33, 0)\text{ in this context?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~d=15t\\&\text{The given equation relates the distance }d\text{, in inches, of an object from its starting position}\\
&\text{to the time }t,\text{ in seconds, since the object started moving. What is the rate of change of}\\&\text{the object’s distance from its starting position over time?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~g(m)=-0.05m+12.1\\
&\text{The given function }g\text{ models the number of gallons of gasoline that remains from a full gas }\\
&\text{tank in a car after driving }m\text{ miles. According to the model, about how many gallons of }\\
&\text{gasoline how many gallons of gasoline are used to drive each mile?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~T(x)=62-8x\\
&\text{The function }T\text{ estimates the temperature, in degrees Fahrenheit (°F),}\text{ in a certain city}\\
&\text{one day in January, where }x\text{ is the number of hours after 10 a.m. and }1\leq x\leq5.\\
&\text{According to the function, what the estimated decrease in temperature each hour, in °F}\\&\mathrm{in~this~city~during~this~time~period?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~w(t)=300-4t\\
&\text{The function }w\text{ models the volume of liquid, in milliliters, in a container }t\text{ seconds after }\\
&\text{it begins draining from a hole at the bottom. According to the model, what is the predicted }\\&\text{volume, in milliliters, draining from the container each second?}\end{aligned}\)

\(\begin{aligned}
&\text{Hana deposited a fixed amount into her bank account each month. The function }f(t)=100+25t\\
&\text{gives the amount, in dollars, in Hana’s bank account after }t\text{ monthly deposits. What is the best}\\
&\text{interpretation of 25 in this context?}\end{aligned}\)

\(\begin{aligned}
&\text{As part of a science experiment on evaporation, Ella measured the height of water in a glass over }\\
&\text{a period of time. The function }f(x)=36-0.16x\text{ gives the estimated height, in centimeters (cm), }\\
&\text{of water in the glass }x\text{ days after the start of the experiment.}\text{ What is the best interpretation of }\\
&0.16\text{ in this context?}\end{aligned}\)

\(\begin{aligned}
&\text{The function }f\text{ defined by }f(t)=14t+9\text{ gives the estimated length, in inches, of a vine plant }\\
&t\text{ months after Tavon purchased it. Which of the following is the best interpretation of 9 in }\\
&\text{this context?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~f(x)=8x+4\\
&\text{The function f gives the estimated height, in feet, of a willow tree }x\text{ years after its height was }\\
&\text{first measured. Which statement is the best interpretation of 4 in this context?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{Kaylani used fabric measuring 5 yards in length to make each suit for a men’s choir. The }\\
&\text{relationship between the number of suits that Kaylani made, }x,\text{ and the total length of} \\
&\text{fabric that she purchased }y,\text{in yards, is represented by the equation }y-5x=6.\text{ What is}\\
&\text{the best interpretation of 6 in this context?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{A family has money in an account for renting movies online. Each time the family rents a movie,}\\
&\text{the cost of the rental is withdrawn from the account, and each rental costs the same amount of }\\
&\text{money. The function }f(m)=21-3m\text{ gives the amount of money, in dollars, in the account after }\\
&\text{the family has rented }m\text{ movies. Which of the following represents the amount of money,}\\
&\text{in dollars, withdrawn from the account each time the family rents a movie?}
\end{aligned}\)

\(\begin{aligned}
&\text{The function }f(x)\text{is defined as 17 more than 3 times a number }x.\text{ If }y = f(x)\text{ is graphed in the }\\
&xy\text{-plane, what is the best interpretation of the }x\text{-intercept?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{Alex engages in up to 3 types of exercise each week for a total of 9 hours while training for a triathlon. }\\
&\text{Alex swims for the same number of minutes each week. The equation }y=540-x-200\text{ represents the}\\
&\text{situation where Alex bikes for }x\text{ minutes during a week and runs for any remaining training time, }y,\\
&\text{in minutes. If this equation is graphed in the }xy\text{-plane, which statement is the best interpretation of the}\\
&x\text{-intercept of the graph?}\\
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p(x)=146-5x\\
&\text{The function }p\text{ shown gives the number of blank sheets of paper, }p(x),\text{ remaining in a}\\
&\text{printer }x\text{ days after the printer had been loaded with paper. Which statement is the}\\
&\text{best interpretation of }p(8)=106?\\
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~T(x)=61-8x\\
&\text{The function }T\text{ estimates the temperature, in degrees Fahrenheit (°F), in a certain city one }\\
&\text{day in January, where }x\text{ is the number of hours after 10 a.m. and }1\leq x\leq7.\text{ What is the best }\\
&\text{interpretation of }T(5)=21\text{ in this context?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x+y=75\\
&\text{The equation above relates the number of minutes, }x,\text{ Maria spends running each day and }\\
&\text{the number of minutes, }y,\text{ she spends biking each day. In the equation, what does the number }\\
&\text{75 represent?}\end{aligned}\)

\(\begin{aligned}
&\text{A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number}\\
&\text{of trees in the neighborhood is 3,934. The equation }2x+35y=3,934\text{ represents this situation. }\\
&\text{Which the following is the best interpretation of }x\text{ in this context?}
\end{aligned}\)

\(\begin{aligned}
&\text{A store sells two different-sized containers of blueberries.The store’s sales of these blueberries}\\
&\text{totaled 896.86 dollars last month. The equation }4.51x+6.07y=896.86\text{ represents this situation,}\\
&\text{where }x\text{ is the number of smaller containers sold and }y\text{ is the number of larger containers sold.}\\
&\text{According to the equation, what is the price, in dollars, of each smaller container?}\end{aligned}\)

\(\begin{aligned}
&\text{At a state fair, attendees can win tokens that are worth a different number of points }\\
&\text{depending on the shape. One attendee won }S\text{ square tokens and }C\text{ circle tokens worth }\\
&\text{a total of 1,120 points. The equation }80S+90C=1,120\text{ represents this situation. }\\
&\text{How many more points is a circle token worth than a square token?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{x}{7}+\frac{y}{5}=\frac{41}{35}\\
&\text{An engineer connects resistors in series, where the resistors in the series have a total}\\
&\text{resistance of }\frac{41}{35}\text{ ohms. In this series, there are }x\text{ resistors of type A, which each have a}\\
&\text{resistance of }a\text{ ohms, and }y\text{ resistors of type B, which each have a resistance of }b\text{ ohms. The}\\
&\text{given equation represents this situation. According to this equation, what is the positive}\\
&\text{difference between the value of }a\text{ and the value of }b?\end{aligned}\)

\(\begin{aligned}
&\text{A school swim team sold shirts to raise money. The team raised \$13 from each short-sleeved shirt}\\
&\text{sold and raised \$14 from each long-sleeved shirt sold. The team raised a total of \$423 from the sale }\\
&\text{of these shirts. The equation }13x+14y=423\text{ represents this situation. Which of the following}\\
&\text{is the best interpretation of }y\text{ in this context?}\end{aligned}\)

\(\begin{aligned}
&\text{Keenan made 32 cups of vegetable broth. Keenan then filled }x\text{ small jars and }y\text{ large jars }\\
&\text{with all the vegetable broth he made. The equation }3x+5y=32\text{ represents this situation. }\\
&\text{Which is the best interpretation of }5y\text{ in this context?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{A total of 271 toothpicks of equal length were used to construct two types of figures: triangles }\\
&\text{and squares. The triangles and squares were constructed so that no two figures had a common }\\
&\text{side. The equation }3x+4y=271\text{ represents this situation, where }x\text{ is the number of triangles}\\
&\text{constructed and }y\text{ is the number of squares constructed. What is the best interpretation of}\\
&(x,y)=(13,58)\mathrm{~in~this~context?}\\
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F(x)=\frac{9}{5}(x-273.15)+32\\
&\text{The function }F\text{ gives the temperature, in degrees Fahrenheit, that corresponds to a}\\
&\text{temperature of }x\text{ kelvins. If a temperature increased by 8.80 kelvins, by how much did}\\&\text{the temperature increase, in degrees Fahrenheit?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c(r)=\frac{2}{5}(2\pi r)\\
&\text{The function }c\text{ gives the partial length, in centimeters (cm), of the circumference of a circle}\\
&\text{with a radius that measures }r\text{ cm. According to the function, for each increase 18 cm in the}\\
&\text{length of radius, this partial length of circumference increases by }k\pi\text{ cm. What is the value}\\&\text{of }k?\end{aligned}\)

\(\begin{aligned}
&\text{A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after}\\
&\text{launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, }\\
&\text{in kg, did the rocket burn each second after launch?}\end{aligned}\)

\(\begin{aligned}
&\text{An agricultural scientist studying the growth of corn plants recorded the height of a}\\
&\text{corn plant at the beginning of a study and the height of the plant each day for the}\\
&\text{next 12 days. The scientist found that the height of the plant increased by an }\\
&\text{average of 1.20 centimeters per day for the 12 days. If the height of the plant on }\\
&\text{the last day of the study was 36.8 centimeters, what was the height, in centimeters,}\\
&\text{of the corn plant at the beginning of the study?}\end{aligned}\)

\(\begin{aligned}
&\text{Hector used a tool called an auger to remove corn from a storage bin at a constant}\\
&\text{rate. The bin contained 24,000 bushels of corn when Hector began to use the auger.}\\
&\text{After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the}\\
&\text{auger continues to remove corn at this rate, what is the total number of hours Hector}\\
&\text{will have been using the auger when 12,840 bushels of corn remain in the bin?}\end{aligned}\)

\(\begin{aligned}&\text{A linear model estimates the population of a city from 1995 to 2019. The}\\&\text{model estimates the population was 59 thousand in 1995, 217 thousand in}\\&\text{2015, and }x\text{ thousand in 2019. To the nearest whole number, what is the}\\&\text{value of }x?\end{aligned}\)

\(\begin{aligned}
&\text{Vivian bought party hats and cupcakes for \$71. Each package of party hats cost \$3,}\\
&\text{and each cupcake cost \$1. If Vivian bought 10 packages of party hats, how many}\\
&\text{cupcakes did she buy?}\end{aligned}\)

\(\begin{aligned}
&\text{A batch of smoothies consists of 4 cups of milk and 2 bananas and has 1,228 milligrams}\\
&\text{(mg) of calcium. There are 304 mg of calcium in 1 cup of milk. How much calcium, in mg,}\\
&\text{is in 1 banana?}\end{aligned}\)