Percents

\(\text{What is }10\%\text{ of 470}?\)

\(\text{What is the }90\%\text{ of }80?\)

\(\text{What is the }20\%\text{ of }440?\)

\(\text{What percentage of 300 is 75?}\)

\(13\text{ is }p\%\text{ of }25.\text{ What is the value of }p?\)

\(\text{If }x>0\text{ and }p\%\text{ of }x\text{ is }13,\text{ which expression represents }x\text{ in terms of }p?\)

\(\text{If }x>0\text{ and }x\text{ is }33\%\text{ of }y,\text{ which expression represents }y\text{ in terms of }x?\)

\(\begin{aligned}&\text{There are 250 trees in a park. Of these trees, }6\%\text{ are birch trees. How many birch trees }\\&\text{are in the park?}\end{aligned}\)

\(\begin{aligned}&\text{A jar has 490 marbles, and } 20\% \text{ of these marbles are blue. How many marbles in the jar are}\\&\text{blue}?\end{aligned}\)

\(\text{Of 300,000 paper clips, 234,000 are size large. What percentage of the paper clips are size large?}\)

\(\text{Out of 300 seeds that were planted, }80\%\text{ sprouted. How many of these seeds sprouted?}\)

\(\begin{aligned}&\text{A scientist analyzed a soil sample with a mass of 900 grams and determined that it}\\&\text{contained 189 grams of water. What is the percentage of water, by mass, in this soil sample?}\end{aligned}\)

\(\begin{aligned}
&\text{Julia purchased 600 feet of fencing. She used }70\%\text{ of this fencing to surround a vegetable }\\
&\text{garden. How many feet of fencing did Julia use to surround the vegetable garden?}
\end{aligned}\)

\(\begin{aligned}&\text{Isabel grows potatoes in her garden. This year, she harvested 760 potatoes and saved }\\&10\%\text{ of them to plant next year. How many of the harvested potatoes did Isabel save }\\&\text{to plant next year?}\end{aligned}\)

\(\begin{aligned}&\text{Levi and Marissa each have stamp collections. The number of stamps in Levi’s collection is}\\&200\%\text{ of the number of stamps in Marissa’s collection. If there are 460 stamps in Marissa’s}\\&\text{collection, how many stamps are in Levis collection?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0.10x+0.20y=0.19(x+y)\\&\text{The equation gives a volume }x\text{, in gallons, of a }10\%\text{ saltwater solution that could be mixed}\\&\text{with a volume }y,\text{in gallons, of a }20\%\text{ saltwater solution to produce a }19\%\text{ saltwater solution.}\\&\text{According to this equation, what volume, in gallons, of the }20\%\text{ saltwater solution could be}\\&\text{mixed with 50.0 gallons of the 10}\%\text{ saltwater solution to produce a 19}\%\text{ saltwater solution?}\\&\text{(Assume that the volume of the mixture is the sum of the volumes of the two solutions}\\&\text{before they were mixed.}\end{aligned}\)

\(\begin{aligned}
&\text{A chemist mixed }x\text{ liters of a }2\%\text{ saline solution with }y\text{ liters of a }5\%\text{ saline solution to}\\
&\text{produce a }3\%\text{ saline solution. Which equation best represents this situation? (Assume}\\&\text{the volumes of the solutions are additive.})\end{aligned}\)

\(\begin{aligned}&\text{How many liters of a }25\%\text{ saline solution must be added to 3 liters of a }10\%\text{ saline solution }\\&\text{to obtain a }15\%\text{ saline solution?}\end{aligned}\)

\(\begin{aligned}
&\text{A biologist mixed a solution that is }0.3\%\text{ sodium chloride by mass with a solution that is}\\
&0.15\%\text{ sodium chloride by mass to obtain a new solution, which has a mass of 80 grams and}\\
&\text{contains 0.21 grams of sodium chloride. How many grams of }0.3\%\text{ sodium chloride solution}\\&\text{did the biologist use?}\end{aligned}\)

\(\begin{aligned}&\text{The table summarizes the number of objects in each group.}\\\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline~\text{ Group }~&\text{ Number of objects }\\\hline\mathrm{A}&325\\\hline\mathrm{B}&68\\\hline\mathrm{C}&572\\\hline\mathrm{D}&102\\\hline\mathrm{Total}&1067\\\hline\end{array}\\\\&\text{The number of objects in group C is }p\%\text{ of the number of objects }\\&\text{in group A. What is the value of }p?\end{aligned}\)

\(0.1242\text{ is }0.09\%\text{ of the number }b.\text{ The number }b\text{ is }25\%\text{ of the number }c.\text{ What is the value of }c?\)

\(\begin{aligned}&\text{The speeds of particles A, B, and C are }a\text{ meters per second, }b\text{ meters per second, and }c\\&\text{meters per second, respectively. If the speed of particle A is }6,000\%\text{ of the speed of particle C}\\&\text{and the speed of particle C is }0.008\%\text{ of the speed of particle B, which expression represents}\\&\text{the value of }a+b\text{ in terms of }c?\end{aligned}\)

\(\begin{aligned}&\text{The positive number }a\text{ is }3,700\%\text{ of the number }c,\text{ and }c\text{ is }20\%\text{ of the number }b.\\&\text{If }a-b=wc,\text{ where }w\text{ is a constant, what is the value of }w?\end{aligned}\)

\(\begin{aligned}&\text{For the positive quantities }h,~j,\text{ and }k,~27\%\text{ of }h\text{ is equivalent to }24\%\text{ of }j,\text{ and }j\text{ is equivalent}\\&\text{to 45}\%\text{ of }k.\text{ What percentage of }k\text{ is }h?\text{ (Disregard the }\%\text{ sign when entering your answer.}\\&\text{For example, if your answer is }39\%,\text{ enter }39)\end{aligned}\)

\(\begin{aligned}&\text{The positive number }a\text{ is }2,800\%\text{ of the number }c,\text{ and }c\text{ is }20\%\text{ of the number }b.\\&\text{What is the value of }a-b,\text{ in terms of }c?\end{aligned}\)

\(\begin{aligned}&\text{The mass of object A is }498\%\text{ of the mass of object B, and the mass of object A is }0.830\% \text{ of}\\&\text{the mass of object C. If the mass of object C is }p\%\text{ of the mass of object B, what is the value of}\\&p?\end{aligned}\)

\(\begin{aligned}&\text{The mass of object A is }416\%\text{ of the mass of object B, and the mass of object A is }0.064\% \text{ of}\\&\text{the mass of object C. If the mass of object C is }p\%\text{ of the mass of object B, what is the value of}\\&\frac{p}{1,000}?\end{aligned}\)

\(\begin{aligned}&\text{The positive number }a\text{ is }2,047\%\text{ of the sum of the positive numbers }b\text{ and }c,\text{ and }b\text{ is }89\%\text{ of}\\&c.\text{ What percent of }b\text{ is }a?\end{aligned}\)

\(\begin{aligned}&\text{While the mass of an object is the same everywhere, the weight of an object is not the same}\\&\text{on different planets. An object has a weight of 170.00 pounds on Earth and a weight of}\\&186.32\text{ pounds on Neptune. The object’s weight on Jupiter is }252.8\%\text{ of its weight on Earth}\\&\text{If the object’s weight on Neptune is }x\%\text{ of its weight on Jupiter, which of the following is}\\&\text{closest to the value of }x?\end{aligned}\)

\(\begin{aligned}&\text{A researcher surveyed undergraduate students, graduate students, and postdoctoral}\\&\text{students. The number of undergraduate students surveyed was }6,950\%\text{ of the number of}\\&\text{post doctoral students surveyed, and the number of graduate students surveyed was }35\%\text { of }\\&\text{the number of undergraduate students surveyed. If there were 4,865 graduate students}\\&\text{surveyed, what was the sum of the number of undergraduate students and postdoctoral}\\&\text{students surveyed?}\end{aligned}\)

\(\begin{aligned}&\text{An entomologist placed an initial population of 40 }Tenebrio~molitor,\text{ a type of beetle, into a}\\&\text{habitat and monitored the population over time. When the number of }Tenebrio~molitor\text{ in}\\&\text{the habitat reached }170\%\text{ of the initial population, the entomologist moved 75}\%\text{ of the}\\&Tenebrio~molitor\text{ to a second habitat. How many }Tenebrio~molitor\text{ did the entomologist move}\\&\text{to the second habitat at this time?}\end{aligned}\)

\(\begin{aligned}&\text{A real estate company offers a series of three webinars. }1,250\text{ people attended the}\\&\text{first webinar. }68\%\text{ of the people who attended the first webinar attended the}\\&\text{second webinar, and }32\%\text{ of the people who attended the first and second webinars}\\&\text{attended the third webinar. How many people attended all three webinars?}\end{aligned}\)

\(\begin{aligned}
&\text{A real estate company offers a series of three webinars. 2,000 people}\\
&\text{attended the first webinar. }65\%\text{ of the people who attended the first webinar}\\
&\text{attended the second webinar, and }44\%\text{ of the people who attended both the}\\
&\text{first and second webinar attended the third webinar. Of those who attended}\\
&\text{the first but did not attend the second webinar, }31\%\text{ attended the third}\\
&\text{webinar. How many people attended both the first and third webinars but did}\\&\text{not attend the second webinar?}\end{aligned}\)

\(\begin{aligned}&\text{At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled }\\&\text{seniors were inducted into the National Honor Society last year. If there were 562 juniors and }\\&\text{602 seniors enrolled at Lincoln High School last year, which of the following is closest to the }\\&\text{total number of juniors and seniors at Lincoln High School last year who }\text{were inducted into }\\&\text{the National Honor Society?}\end{aligned}\)

\(\begin{aligned}&\text{On a plot of land, }52.0\%\text{ of the square footage is farmland and the remaining}\\
&\text{square footage is pasture. There are buildings on exactly }21.5\%\text{ of the square }\\
&\text{footage of the farmland, and there are buildings on exactly }14.0\%\text{ of the square }\\&\text{footage of the pasture.}\text{ If there are buildings on exactly }
p\%\text{ of the square footage of }\\&\text{the plot of land, what is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\text{A car dealership has only sedans, SUVs, and minivans for sale. On Monday, }30\%\text{ of the vehicles}\\
&\text{for sale were sedans and }50\%\text{ were SUVs. If there 57 sedans for sale at the dealership on Monday,}\\
&\text{how many minivans were for sale?}\end{aligned}\)

\(\begin{aligned}&\text{A school district is forming a committee to discuss plans for the construction of a new }\\&\text{high school. Of those invited to join the committee, 15}\%\text{ are parents of students, 45}\%\\&\text{are teachers from the}\text{ current high school, 25}\%\text{ are school and district administrators,} \\&\text{and the remaining 6 individuals are students. How many more teachers were invited }\\&\text{to join the committee than school and districtadministrators?}\end{aligned}\)

\(\begin{aligned}
&\text{When a collection of books is sorted, }52\%\text{ are nonfiction and the remaining books are}\\
&\text{fiction. Of those that are fiction, }75\% \text{ are westerns and the remaining fiction books are}\\
&\text{romance. If there are 933 romance books in this collection, what is the total number of}\\&\text{books in the collection?}\end{aligned}\)

\(\begin{aligned}&\text{The composition of an animal is defined as the muscles, bones, and fat of the animal. A}\\&\text{scientist studied the composition of one young swamp buffalo and determined the buffalo}\\&\text{had 139.2 kilograms of muscle, which made up approximately }67. 7\%\text{ of its composition. Of}\\&\text{the remaining composition of this buffalo, approximately }51.4\%\text{ was bone, and the}\\&\text{remainder was fat. Based on these approximations, to the nearest tenth, how many}\\&\text{kilograms of this buffalo’s composition was bone?}\end{aligned}\)

\(\begin{aligned}&\text{The population of Greenville increased by }7\%\text{ from 2015 to 2016. If the 2016 population}\\&\text{is }k\text{ times the 2015 population, what is the value of }k?\end{aligned}\)

\(\begin{aligned}
&\text{A gallery had }x\text{ artifacts in a collection. When more artifacts were added to the collection,}\\
&\text{number of artifacts increased by }149\%.\text{ What is the number of artifacts in the collection }\\&\text{in terms of }x?\end{aligned}\)

\(\begin{aligned}&\text{The percent increase in mass of a certain red kangaroo from 90 days old to 160 days old was }438\%.\\&\text{If this red kangaroo’s mass was }k\text{ grams at 90 days old, which expression represents its mass, }\\&\text{in grams, at 160 days old?}\end{aligned}\)

\(210\text{ is }p\%\text{ greater than 30. What is the value of }p?\)

\(\begin{aligned}
&\text{At a hotel, guests used the pool for a total of }t\text{ hours in March. At the same hotel, guests used the }\\&\text{pool for }3.49t\text{ hours in April. What is the percent increase in the number of hours guests used the }\\&\text{pool from March to April?}\end{aligned}\)

\(\begin{aligned}&\text{The expression }0.33x\text{ represents the result of decreasing a positive quantity }x\text{ by what }\\&\text{percent?}\end{aligned}\)

\(\begin{aligned}&\text{In 2010, a skating team had a total of 35 skaters, each classified as either advanced or}\\&\text{intermediate. From 2010 to 2020, the number of advanced skaters on the team increased}\\&\text{by approximately }53\%\text{, and the number of intermediate skaters on the team increased by}\\&\text{approximately }44\%.\text{ The total number of skaters on the team increased by approximately}\\&49\%.\text{Which equation best represents this situation, where }a\text{ are presents the number of}\\&\text{advanced skaters on the team in 2010 and }b\text{ represents the number of intermediate skaters}\\&\text{on the team in 2010?}\end{aligned}\)

\(\begin{aligned}
&\text{The combined original price for a towel and chair is }\$36.\text{ After a }45\%\text{ discount to the }\\
&\text{chair and a }25\%\text{ discount to the towel are applied, the combined sale price for the two}\\
&\text{items is \$25. Which system of equation gives the original price }t\text{ in dollars of the}\\
&\text{towel and }c\text{ in dollars of the chair?}\end{aligned}\)

\(\begin{aligned}&\text{The result of increasing the quantity }x \text{ by }400\%\text{ is }60.\text{ What is the value of }x?\end{aligned}\)

\(\begin{aligned}&\text{The result of increasing the quantity }x \text{ by }1800\%\text{ is }684.\text{ What is the value of }x?\end{aligned}\)

\(\begin{aligned}&\text{Katarina is a botanist studying the production of pears by two types of pear trees. She noticed }\\&\text{that Type A trees produced 20 percent more pears}\text{than Type B trees did. Based on Katarina’s}\\&\text{observation, if the Type A trees produced 144 pears, how many pears did the Type B trees }\\&\text{produce?}\end{aligned}\)

\(\begin{aligned}&\text{A scientist studying the life cycle of butterflies counted the number of butterflies in a}\\&\text{certain habitat each day for 46 days. On June 15, there were 168 butterflies in the habitat.}\\&\text{The percent increase in the number of butterflies in the habitat from May 1 to June 15 was}\\&31.25\%.\text{ How many butterflies were in the habitat on May 1?}\end{aligned}\)

\(\begin{aligned}&\text{After }20\%\text{ of the original number of objects in a group were removed from the group,}\\&180\text{ objects remained in the group. How many objects were removed from the group?}\end{aligned}\)

\(\begin{aligned}&\text{A rectangular banner has an area of 2,300 square inches. A copy of the banner is made in}\\&\text{which the length and width of the original banner are each increased by 20}\%.\text{ What is the}\\&\text{area of the copy, in square inches?}\end{aligned}\)

\(\begin{aligned}&\text{The positive quantity }r\text{ is increased by }20\%,\text{ and then the resulting quantity is }\\
&\text{decreased by 25}\%.\text{ Which expression represents the result of these two changes?}\end{aligned}\)

\(\begin{aligned}&\text{The value of an autographed baseball increased by }178\%\text{ from the end of 2012 to the end of}\\&2013\text{ and then decreased by }21\%\text{ from the end of 2013 to the end of 2014. What was the net}\\&\text{percentage increase in the value of the autographed baseball from the end of 2012 to the}\\&\text{end of 2014?}\end{aligned}\)

\(\begin{aligned}&\text{A rectangle was altered by increasing its length by 10 }\%\text{ and decreasing its width by }p \%.\\&\text{If these alterations decreased the area of the rectangle 12}\%\text{, what is the value of }p?\end{aligned}\)

\(\begin{aligned}&\text{The number }a\text{ is }110\%\text{ greater than the number }b.\text{ The number }b\text{ is }90\%\text{ less than }47.\\&\text{What is the value of }a?\end{aligned}\)

\(\begin{aligned}&\text{A number }f\text{ is }120\%\text{ greater than a positive number }g.\text{ A number }h\text{ is }90\%\text{ less than the}\\
&\text{number }f.\text{The number }h\text{ is how many times the number }g?\end{aligned}\)

\(\begin{aligned}&\text{In 2008, Zinah earned }14\%\text{ more than in 2007, and in 2009 Zinah earned }4\%\text{more than in }\\&\text{2008. If Zinah earned }y\text { times as much in 2009 as in 2007, what is the value of }y?\end{aligned}\)

\(\begin{aligned}&\text{In 2013, Chloe earned }11\%\text{ more than in 2012, and in 2014 Chloe earned }6\%\text{ more than in }\\&\text{2013. If Chloe earned }y\text { times as much in 2012 as in 2014, which of the following is closest}\\&\text{to the value of }y?\end{aligned}\)

\(\begin{aligned}
&\text{A scientist studied the effects of mixing two chemicals, chemical A and chemical B, by }\\
&\text{gradually adding more of each chemical to a mixture of the two chemicals. At the start }\\
&\text{of the study, the mass of chemical A in the mixture was equal to the mass of chemical B }\\
&\text{in the mixture. From the start of the study to the end of the study, the mass of chemical A}\\
&\text{in the mixture increased by 2,600}\%\text{ and the mass of chemical B in the mixture increased }\\
&\text{by }380\%. \text{ At the end of the study,}\text{ approximately how many times greater was the mass of }\\
&\text{chemical A in the mixture than the mass of chemical B in the mixture?}\end{aligned}\)

\(\begin{aligned}&\text{A researcher investigated two species of mites: a predator and its prey. At the start of a week,}\\&\text{there was an equal number of the two species. At the end of the week, the number of prey}\\&\text{had increased by 2,700}\%\text{ of the number of prey at the start of the week, and the number of}\\&\text{predators had increased by }180\% \text{ of the number of predators at the start of the week. The}\\&\text{number of prey at the end of the week was }p\%\text{ greater than the number of predators at the}\\&\text{end of the week. What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&\text{The regular price of a shirt at a store is }\$11.70. \text{ The sale price of the shirt is 80}\%\text{ less than}\\
&\text{the regulare price, and the sale price is 30}\%\text{ greater than the store’s cost for the shirt. What }\\&\text{was the store’s cost, in dollars, for the shirt?}\end{aligned}\)

\(\begin{aligned}&\text{A clothing store buys shirts at a wholesale price of 4.00 dollars each and resells them}\\
&\text{each at a retail price that is }280\% \text{ of the wholesale price. At the end of the season, }\\
&\text{any remaining shirts are marked at a discounted price that is 80}\%\text { off the retail price. }\\&\text{What is the discounted price of each remaining shirt, in dollars?}\end{aligned}\)