Writing Equations (One Variable)

\(\begin{aligned}
&\text{3 more than 8 times a number }x\text{ is equal to 83. Which equation represents }\\
&\text{this situation?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{When 4 times the number }x\text{ is added to 12 }\text{, the result is 8.}\\
&\text{What number results when 2 times }x\text{ is added to 7}?\end{aligned}\)

\(\begin{aligned}
&\text{If }16+4x\text{ is 10 more than 14, what is the value of }8x?\end{aligned}\)

\(\begin{aligned}&\mathrm{For~a~set~of~three~consecutive~integers,~the~result~of~subtracting~the~greatest~integer~from~the}\\&\mathrm{sum~of~the~other~two~integers~is~48.~What~is~the~value~of~the~greatest~of~the~three~integers?}\end{aligned}\)

\(\begin{aligned}&\text{Cathy has }n\text{ CDs. Gerry has 3 more than twice the number of CDs that Cathy has. In}\\&\text{terms of }n,\mathrm{how~many~CDs~does~Gerry~have?}\end{aligned}\)

\(\begin{aligned}
&\text{A company that manufactures staplers calculates its monthly profit, in dollars, by }\\
&\text{subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The}\\
&\text{equation }11,000=2.00x-6,500\text{ represents this situation for a month where }x\text{ staplers }\\
&\text{are manufactured and sold. Which statement is the best interpretation of 2.00}x\text{ in this }\\
&\text{context?}\end{aligned}\)

\(\begin{aligned}
&\text{To purchase a used car at a total price of 14,000 dollars, a one-time down payment is}\\
&\text{required, and then fixed monthly payments are made for the remaining amount owed for}\\
&\text{the car. The equation }14, 000=2, 800+200t\text{ represents this situation, where }t\text{ is the}\\
&\text{number of fixed monthly payments that are made. Which of the following is the best}\\
&\text{interpretation of 200 in this context?}\end{aligned}\)

\(\begin{aligned}
&\text{To make a bookcase, a worker charged a onetime fee plus }\$17\text{ per hour worked. The}\\
&\text{equation }17h+45=164\text{ represents this situation, where }h\text{ is the number of hours}\\
&\text{worked. Which of the following is the best interpretation of 164 in this context?}\end{aligned}\)

\(\begin{aligned}
&\text{John paid a total of \$165 for a microscope by making a down payment of \$37 plus }\\
&p \text{ monthly payments of \$16 each. Which of the following equations represents this }\\&\text{situation?}\end{aligned}\)

\(\begin{aligned}
&\text{Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo }\\
&\text{paid \$2 for the box of cereal and \$1.90 per pound for the strawberries. If Lorenzo paid }\\
&\text{a total of \$9.60 for the box of cereal and the strawberries, which of the following equations}\\
&\text{can be used to find }p\text{, the number of pounds of strawberries Lorenzo purchased?}\\
&\text{(Assume there is no sales tax.)}\end{aligned}\)

\(\begin{aligned}
&\text{Jaqueline spent \$150 for supplies and gas to start a lawn-mowing service. She charges}\\
&\$25\text{ for each lawn she mows. In the first week Jaqueline made \$50 after the cost of}\\
&\text{supplies and gas was deducted. Which equation represents this situation, where }x\\
&\text{is the number of lawns Jaqueline mowed during the first week?}\end{aligned}\)

\(\begin{aligned}&\text{A machine makes 9-inch, 8-inch, and 3-inch parts. During a certain day, the number of 9-}\\&\text{inch parts that the machine makes is 4 times the number }n\text{ of 8-inch parts, and the number}\\&\text{of 3-inch parts is 15. During this day, the machine makes 100 parts total. Which equation}\\&\mathrm{represents~this~situation?}\end{aligned}\)

\(\begin{aligned}&\text{The cost to rent a bus from Company X is \$950 for the first 2 hours and an additional \$50}\\&\text{per hour for each hour after the first 2 hours. If the total cost to rent the bus from Company }\\&\text{X for }t\text{ hours, where }t > 2 \text{, is \$1,250, which equation represents this situation?}\end{aligned}\)

\(\begin{aligned}
&\text{Rectangle P has an area of 72 square inches. If a rectangle with an area of 20 square inches}\\
&\text{is removed from rectangle P, what is the area, in square inches, of the resulting figure?}\end{aligned}\)

\(\begin{aligned}
&\text{A total of 165 people contributed to a charity event as either a donor or a volunteer. }\\
&\text{130 people contributed as a donor. How many people contributed as a volunteer?}\end{aligned}\)

\(\begin{aligned}
&\text{A chemist combines water and isopropanol to make a mixture with a volume of }\\
&\text{52 milliliters (mL). The volume of isopropanol in the mixture is 10 mL. What is the}\\
&\text{volume of water, in mL, in the mixture?(Assume that the volume of the mixture is the sum}\\
&\text{of the volumes of water and isopropanol before they were mixed.)}\end{aligned}\)

\(\begin{aligned}
&\text{Nasir bought 9 storage bins that were each the same price. He used a coupon for \$63 off the entire}\\
&\text{purchase. The cost for the entire purchase after using the coupon was \$27. What was the original }\\
&\text{price, in dollars, for 1 storage bin?}\end{aligned}\)

\(\begin{aligned}
&\text{A proposal for a new library was included on an election ballot. A radio show stated that }\\
&\text{3 times as many people voted in favor of the proposal as people who voted against it.}\\
&\text{A social media post reported that 15,000 more people voted in favor of the proposal than }\\
&\text{voted against it. Based on these data, how many people voted against the proposal?}\end{aligned}\)

\(\begin{aligned}
&\text{On the first day of a semester, a film club has 90 members. Each day after the first day of the}\\
&\text{semester, 10 new members join the film club. If no members leave the film club, how many}\\
&\text{total members will the film club have 4 days after the first day of the semester?}\end{aligned}\)

\(\begin{aligned}
&\text{A manager is responsible for ordering supplies for a shaved ice shop. The shop’s inventory starts }\\
&\text{with 4,500 paper cups, and the manager estimates that 70 of these paper cups are used each day. }\\
&\text{Based on this estimate, in how many days will the supply of paper cups reach 1,700?}\end{aligned}\)

\(\begin{aligned}
&\text{Brian saves }\frac{2}{5}\text{ of the \$215 he earns each week from his job. If Brian continues to save at }\\
&\text{this rate, how much money, in dollars, will Brian save in 9 weeks?}\end{aligned}\)

\(\begin{aligned}
&\text{In August, a car dealer completed 15 more than 3 times the number of sales the car dealer}\\
&\text{completed in September. In August and September, the car dealer completed 363 sales.}\\
&\text{How many sales did the car dealer complete in September?}\end{aligned}\)

\(\begin{aligned}&\text{Last week Raul worked 11 more hours than Angelica. If they worked a combined }\\
&\text{total of 59 hours, how many hours did Angelica work last week?}\end{aligned}\)

\(\begin{aligned}&\text{A librarian has 43 books to distribute to a group of children. If he gives each child 2}\\
&\text{books, he will have 7 books left over. How many children are in the group?}\end{aligned}\)

\(\begin{aligned}
&\text{A bowl contains 20 ounces of water. When the bowl is uncovered, the amount of water in the}\\
&\text{bowl decreases by 1 ounce every 4 days. If 9 ounces of water remain in this bowl, for how many}\\
&\text{days has it been uncovered?}\end{aligned}\)

\(\begin{aligned}
&\text{Henry receives a \$60.00 gift card to pay for movies online. He uses his gift card to buy 3 movies}\\
&\text{for \$7.50 each. If he spends the rest of his gift card balance on renting movies for \$1.50 each,}\\&\text{how many movies can Henry rent?}\end{aligned}\)

\(\begin{aligned}
&\text{A gym charges its members a onetime \$36 enrollment fee and a membership fee of \$19 per month.}\\&\text{If there are no charges other than the enrollment fee and the membership fee, after how many}\\&\text{months will a member have been charged a total of \$188 at the gym?}\end{aligned}\)

\(\begin{aligned}
&\text{A website-hosting service charges businesses a onetime setup fee of \$350 plus }d \text{ dollars }\\
&\text{for each month. If a business owner paid \$1,010 for the first 12 months, including the}\\
&\text{setup fee, what is the value of }d ?\end{aligned}\)

\(\begin{aligned}
&\text{A partially filled pool contains 600 gallons of water. A hose is turned on, and water flows into }\\
&\text{the pool at the rate of 8 gallons per minute. How many gallons of water will be in the pool after }\\&\text{70 minutes?}\end{aligned}\)

\(\begin{aligned}
&\text{In a video game, each player starts the game with }k\text{ points and loses 2 points each time a}\\
&\text{task is not completed. If a player who gains no additional points and fails to complete }\\
&\text{100 tasks has a score of 200 points, what is the value of }k ?\end{aligned}\)

\(\begin{aligned}&\text{A park rents beach umbrellas to visitors. The park earns revenue of \$16 for each beach}\\&\text{umbrella they rent for the day. On Wednesday, the park earned \$400 in profit from renting}\\&\text{beach umbrellas after paying daily expenses of \$144. How many beach umbrellas did the}\\&\mathrm{park~rent~on~Wednesday?~(profit=total~revenue-total~expenses)}\end{aligned}\)