Word Problem Practice Answer Key

Name: Key Pd: Date: Real-Life Applications Lin is tracking the progress of her plant's growth. Today the plant is 5 cm high. The plant grows 1.5 cm per day. a. Write a linear model that represents the height of the plant after d days. [h = 1.5d + 5]   b. What will the height of the plant be after 20 days? [h = 1.5(20) + 5] [h = 30 + 5] [h = 35] (35 cm) [circled] Mr. Thompson is on a diet. He currently weighs 260 pounds. He loses 4 pounds per month. a. Write a linear model that represents Mr. Thompson's weight after m months. [w = -4m + 260]   b. After how many months will Mr. Thompson reach his goal weight of 220 pounds? [220 = -4m + 260] [-40 = -4m] [10 = m] 10 months [circled] Paul opens a savings account with $350. He saves $150 per month. Assume that he does not withdraw money or make any additional deposits. a. Write a linear model that represents the total amount of money Paul deposits into his account after m months. [a = 150m + 350]   b. After how many months will Paul have more than $2,000? [2000 = 150m + 350] [1650 = 150m] [11 = m] 11 months [circled] 4) The population of Bay Village is 35,000 today. Every year the population of Bay Village increases by 750 people. a. Write a linear model that represents the population of Bay Village x years from today. \[p = 750x + 35000\] b. In approximately many years will the population of Bay Village exceed 50,000 people? \[50000 = 750x + 35000\] \[15000 = 750x\] \[20 = x\] 20 years it will reach 50,000 ppl, 21 years will exceed 50,000 ppl [circled] (*) 5) Biologists have found that the number of chirps some crickets make per minute is related to temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.   a. Write a linear model that shows the number of cricket chirps a minute, d, in terms of temperature, t. (68, 124) (80, 172) \[\frac{172 - 124}{80 - 68} = \frac{48}{12} = 4\] \[y = 4x + b\] \[124 = 4(68) + b\] \[b = -148\] \[c = 4t - 148\] b. How warm is it when the crickets are chirping 150 times a minute? \[150 = 4t - 148\] \[298 = 4t\] \[74.5 = t\] \[74.5^{\circ}\] [boxed] Conner has $25,000 in his bank account. Every month he spends $1,500. He does not add money to the account. a. Write a linear model that shows how much money will be in the account after x months. [m = -1500x + 25000]   b. How much money will Conner have in his account after 8 months? [m = -1500(8) + 25000] [m = -12000 + 25000] [m = 13000] $13000 [boxed] A cell phone plan costs $30 per month for unlimited calling plus $0.15 per text message. a. Write a linear model that represents the monthly cost of this cell phone plan if the user sends t text messages. [c = 0.15t + 30]   b. If you send 200 text messages, how much would you pay according to this cell phone plan? [c = 0.15(200) + 30] [c = 30 + 30] [c = 60] $60 [boxed] Ben walks at a rate of 3 miles per hour. He runs at a rate of 6 miles per hour. In one week, the combined distance that he walks and runs is 210 miles.   a. Write a linear model that relates the number of hours that Ben walks to the number of hours Ben runs. [3w + 6r = 210]   b. Ben runs for 25 hours. For how many hours does he run? [3w + 6(25) = 210] [3w + 150 = 210] [3w = 60] [w = 20] 20 hours running [circled] A salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year. a. Write a linear model that shows the salesperson's total income based on total sales of k dollars. [T = 0.1k + 35000]   b. If the salesperson sells $250,000 worth of merchandise, what is her total income for the year, including her base salary? [T = 0.1(250,000) + 35,000] [T = 25,000 + 35,000] [T = 60,000] $60,000 [boxed]   Amery has x books that weigh 2 pounds each and y books that weigh 3 books each. The total weight of his books is 60 pounds. a. Write a linear model that relates the number of 2 pound books to the number of 3 pound books Amery has. [2w + 3h = 60]   b. If Amery has 10 3-pound books, how many 2-pound books does he have? [2w + 3(10) = 60] [2w + 30 = 60] [2w = 30] [w = 15] 15, 2-lb books [circled] Max sells lemonade for $2 per cup and candy for $1.50 per bar. He earns $425 selling lemonade and candy. a. Write a linear model that relates the number of cups of lemonade he sold to the number of bars of candy he sold. [2c + 1.5b = 425]