6. Linear function word problems.docx

LEVEL 2 1. Vendors at a craft fair pay $45 to rent a table for the day. Benjamin rents a table at the craft fair and sells 8 ounce jars of jam for $7.95 per jar. If it costs Benjamin $2.75 to make each container of jam, which of the following equations best models his profit, p, from one day at the craft fair if he sells n jars of jam? A. p=5.20n B. p=7.95n C. p=5.20n-45 D. p=7.95n-45 Correct answer: C 2. John manufactures household furniture. His start-up costs, including tools, plans, and advertising, total $5000. Labor and materials for each piece of furniture total $350, and his production costs are the sum of his start-up costs plus the cost of labor and materials. If John makes f pieces of furniture, what will be his production costs, c, in dollars? A. f=350c+5000 B. c=350f+5000 C. f=5000c+350 D. c=5000f+350 Correct answer: B 3. The number of problems assigned as homework by a savvy math professor is a function of the length of the class on a particular day, which is either 45 minutes, 90 minutes, or 135 minutes. He first multiplies the number of minutes by 4 and then divides that number by 9. Finally, he subtracts 12 from that amount. Which of the following functions best represents the number of math problems the professor assigns depending on the length of the class, t, in minutes? A. f(t)=​9​​4​​t−12 B. f(t)=​9​​4​​(t−12) C. f(t)=12−​9​​4​​t D. f(t)=12+​9​​4​​t Correct answer: A 4. Imani's grandmother's house is 5 miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at 10 miles per hour. Which equation best describes the distance, d, in miles, Imani is from home after t hours? A. d=5+10t B. d=5−10t C. d=5t+10 D. d=5t−10 Correct answer: A 5. Hiroto spends $68 on e-books and paperback books combined. Each e-book he buys costs $5, and each paperback book he buys costs $12. If Hiroto buys x e-books and y paperback books, which of the following equations best models the situation? A. 5x+12y=68 B. 12x+5y=68 C. 17(x+y)=68 D. 17xy=68 Correct answer: A 6. A construction company's fees include a flat daily charge to come to a work site, in addition to a constant hourly rate. Any fractional hours are charged at that fraction of the hourly rate. Additionally, if a job takes less than 10 hours to complete, it is completed in one day. According to these rules, a 3.5 hour job would cost $250 and an 8 hour job would cost $475. If the construction company completes a job in one day, which of the following functions best models the cost, c, in dollars, for an h hour job? A. c(h)=50h B. c(h)=60h C. c(h)=50h+75 D. c(h)=60h+10 Correct answer: C 7. From 2005 to 2013, the population of Belize has been increasing by approximately 7,500 people per year. The population of Belize in 2010 was 308,595. If t stands for years since 2005, which of the following functions best models the population, p, of Belize during this time period? A. p(t)=271,095+7,500t B. p(t)=308,595+7,500t C. p(t)=346,095+7,500t D. p(t)=−14,728,905+7,500t Correct answer: A 8. In a political science class, test scores were determined to be 20 times the number of hours, h, the student studied plus 3. Which of the following functions best describes a student’s test score depending on the number of hours, h, that the student studied? A. f(h)=3h+20 B. f(h)=20h C. f(h)=60h D. f(h)=20h+3 Correct answer: D 9. A 300-room hotel collects $75 per occupied room and does not collect any money for vacant rooms. Which of the following functions best represents how many dollars, d, the hotel generates given the number of vacant rooms in the hotel, v? A. d=75(300−v) B. d=75(300+v) C. d=300(75−v) D. d=300(75+v) Correct answer: A LEVEL 3 1. Dalia makes a cranberry apple punch that contains 20% real juice by mixing x gallons of a cranberry drink with y gallons of an apple drink. The cranberry drink contains 40% real juice and the apple drink contains 10% real juice. Which of the following equations represents the relationship between x and y? A. 0.4x+0.1y=20 B. 0.4x+0.1y=x+y C. 0.20(x+y)=x+y D. 0.2(x+y)=0.4x+0.1y Correct answer: D 2. Gary learned that the value of his car depreciates by 15% per year. Which of the following functions best describes the value of his car the year after the car is worth m dollars? A. f(m)=0.15m B. f(m)=0.85m C. f(m)=1−0.15m D. f(m)=1−0.85m Correct answer: B 3. Javier has a cell phone plan that allows him to use up to 4 gigabyte (GB) of data per month. Streaming videos is the only action he does on his phone which uses up this data. Each time he streams a video, the amount of gigabytes of his phone's data plan decreases. Specifically, his cell phone company estimates that approximately 0.12 GB of data are used for every 30minutes of video streaming. If Javier has spent m minutes this month streaming videos, which of the following best approximates the amount of data, d, he has remaining on his plan? A. d=4−0.12m B. d=4+0.12m C. d=4−0.004m D. d=4+0.004m Correct answer: C 4. Li Jing has already read 13​​ of her 384 page book. She figures that she reads at a constant rate and can read about 45 pages in 11 hour. If mm is the amount of time, in minutes, that Li Jing has spent reading the final 23​​ of the book, which of the following best approximates the number of pages, p, that she has left? A. p=128−45m B. p=256−45m C. p=128−​4​​3​​m D. p=256−​4​​3​​m Correct answer: D 5. Between 2008 and 2012, the revenue obtained from digital music album downloads, r, in millions of dollars, in the United States increased by approximately 132 million dollars per year. In 2010, the digital music revenue in the U.S. was about 872 million dollars. If  t represents years since 2008, which of the following best models the situation for 0≤t ≤4? A. r(t)=132t B. r(t)=132t+608 C. r(t)=132t+872 D. r(t)=132t+1136 Correct answer: B 6. David's vehicle has a 21 gallon gas tank. If he drives only on highways, he can go about 525miles on one tank of gas. If he drives only in the city, he can go about 378 miles on one tank of gas. David drove 455 miles on his last tank of gas. If x is the amount of gallons used on highway driving and y is the gallons used on city driving, which of the following best models the relationship between x and y in this situation? A. 25x+18y=21 B. 25x+18y=455 C. 525x+378y=21 D. 525x+378y=455 Correct answer: B 7. Mikayla is a waitress who makes a guaranteed $50 per day in addition to tips of 20% of all her customer receipts, t. She works six days per week. Which of the following functions best represents the amount of money that Mikayla makes in one week? A. f(t)=50+20t B. f(t)=300+20t C. f(t)=50+0.2t D. f(t)=300+0.2t Correct answer: D 8. John's seafood restaurant is trying to estimate its profits. John has found that on average, each meal served costs the restaurant $14.56 and takes in $17.12. John has also found that on average, each beverage served costs the restaurant $1.20 and takes in $5.40. If c customers order a meal, and half of those customers order a beverage, which of the following functions models the restaurant's total profit? A. f(c)=17.12c−14.56c+5.40(​12​​c)−1.20(​12​​c) B. f(c)=17.12c−14.56c+5.40c−1.20c C. f(c)=14.56c−17.12c+1.20c−5.40c D. f(c)=14.56c−17.12c+1.20(​​12​​c)−5.40(​​12​​c) Correct answer: A LEVEL 4 1. Maria burns about 600 calories per hour jogging and about 450 calories per hour biking. If Maria spends x hours per day biking, and 45​​ as much time jogging, which of the following functions best models the amount of calories, C, that Maria burns in one day from jogging and biking? A. C(x)=840x B. C(x)=930x C. C(x)=960x D. C(x)=1050x Correct answer: B 2. Mikayla walked nine miles in three hours. She walked f miles during the first hour and 23​​ of the remaining distance during the second hour. Which of the following functions best represents the number of miles in the third hour, t, she had to walk in terms of the number of miles she walked in the first hour, f ? A. t=3 B. t=3−​13​​f C. t=3+​23​​f D. t=3+f Correct answer: B 3. The gas tank in Ms. Brown's car holds a total of 15 gallons. At any given time, how many gallons, g, will Ms. Brown have to pump into her car to fill her tank given the fraction of the tank, f, already filled? A. g=15f B. g=​15f​​ C. g=15−15f D. g=15−​​15f​​ Correct answer: C 4. Sterling silver is an alloy of silver that is 92.5% pure silver. If x grams of sterling silver are mixed with y grams of an 88% silver alloy to produce a 91% silver alloy, which of the following equations correctly relates x and y? A. 0.075x+.12y=0 B. 0.015x−0.03y=0 C. 0.925x+0.88y=91 D. 0.925x+0.88y=0.91xy Correct answer: B 5. A roller coaster is currently traveling at a speed of 49 miles per hour (mph). The coaster’s speed will increase at a constant rate of 17mph every 2 seconds until the coaster reaches its top speed 5 seconds from now. If t≤5, which function best represents the roller coaster’s speed, in miles per hour, t seconds from now? A. f(t)=49+8.5t B. f(t)=49+17t C. f(t)=49t+9.8t D. f(t)=49t+17t Correct answer: A 6. Gustav is starting a special sprinting regimen in outdoor track. The regimen suggests sprinting for a certain number of seconds, s, at first. The second time he sprints, he should run 150 more seconds than the first time. For the third time, the regimen suggests sprinting twice the number of seconds as the first time. Finally, the regimen suggests an 80-second sprint. Which of the following functions can be used to find the total number of seconds, t, suggested by the entire sprinting regimen? A. t=s+230 B. t=2s+230 C. t=​​​52​​s+230 D. t=4s+230 Correct answer: D 7. In 2007, approximately 50% of the world's population lived in rural (defined as non-urban) areas. From 2005 to 2013, the percent of the world's population living in rural areas decreased by about 0.5 percentage points per year. If t represents years since 2005, which of the following equations best models the percent of the world's population living in rural areas, r, from 2005 to 2013? A. r−50=−0.5(t−2) B. r−50=−0.5(t−7) C. r−2=−0.5(t−50) D. r−7=−0.5(t−50) Correct answer: A 8. Maria burns about 600 calories per hour jogging and about 450 calories per hour biking. If Maria spends x hours per day biking, and ​​​45​​ as much time jogging, which of the following functions best models the amount of calories, C, that Maria burns in one day from jogging and biking? A. C(x)=840x B. C(x)=930x C. C(x)=960x D. C(x)=1050x Correct answer: B