College Prep Algebra
HW Lesson 3.7B: Applications of Linear Equations
Write and solve a linear equation for each of the following application problems.
1. Ms. Adams has 32 ounces of water in a bottle. She can drink 5 ounces an hour.
a. How much water does she have left after n hours?
b. How many hours will it take her to finish the bottle of water?
2. At a party store, helium balloons cost 79 cents each and a box of favors costs $11.95.
You have $40 to spend and you need two boxes of favors. How many balloons can you
buy? There is no sales tax.
3. A chemist has solutions of hydrochloric acid in two different concentrations. One solution
has 10 moles per liter; the other has 2.5 moles per liter. She mixes x liters of the first
solution and y liters of the second solution.
a. How many moles of acid are in x liters of the first solution?
b. How many moles of acid are in y liters of the second solution?
c. How many moles of acid are in the mixture?
d. The chemist wants to have 6 moles of acid in the final mixture. She uses 1 liter of the
second solution. How many liters of the first solution should she use?
4. Card Carriers charges $36 to print 1200 business cards and $56 for 2700 cards. Assume
the relationship between the price and the number of business cards is linear.
a. Write an equation giving price as a function of the number of cards printed.
b. Find the set-up cost (the cost of printing 0 cards).
c. Find the cost of printing 6000 cards.
5. The temperature of an oven is 350 F before being turned off. The temperature drops at
a constant rate to 190 F in 20 minutes.
a. Convert the rate of change to F per minute.
b. Find how long it takes for the oven to cool to 150 F.
6. At a produce market, Granny Smith apples are $0.75 a pound and Red Delicious apples
are $0.95 a pound. Jim has $9 and buys 3 pounds of Granny Smith apples. Round
answers to the nearest pound.
a. How many pounds of Red Delicious apples can he buy?
b. If the price of each kind of apple increases $0.11 per pound, how many pounds of Red
delicious apples can he buy?
7. A chemist mixed A ounces of a 30% chlorine solution with B ounces of a 40% chlorine
solution. The final mixture contained 18 ounces of chlorine. Write an expression to model
8. Last week, Mr. Chinn sold $20,000 worth of newspaper advertisements and earned $800.
The week before, he sold $26,000 worth of advertisements and earned $860. Assume the
relationship between Mr. Chinn’s weekly earnings and the value of the advertisements he
sells is linear.
a. Write an equation giving Mr. Chinn’s weekly earnings as a function of the value of the
advertisements he sells.
b. In this situation, what do the slope and y-intercept mean?
c. If in one week, Mr. Chinn sells $30,000 worth of advertisements, how much will he
9. Mr. Reyes bought 5 pounds of coffee. On the average, he uses one-fifth of a pound a
a. Write an equation relating the pounds of coffee c he has left after w weeks.
b. During what week will he likely run out of coffee?
10. Helene bought L 74-minute recordable CDs at $0.58 each and M 80-minute recordable
CDs at $0.95 each. Suppose she spent $12.40 and bought ten 80-minute CDs. How
many 74-minute CDs did she buy?
In 11 and 12, consider the following information. On a quiz show, 20 points are given for
correct answers to regular questions and 50 points are given for correct answers to bonus
11. If a contestant answers 5 regular questions correctly and 7 bonus questions correctly,
how many points does she have?
12. Suppose a contestant earned 650 points.
a. If she answered 13 bonus questions correctly, how many regular questions did she
b. If she answered 25 regular questions correctly, how many bonus questions did she
13. The Kelvin temperature scale is often used by scientists who work with very cold
materials. Water freezes at 32 F or 273 K. Water boils at 212 F or 373 K. What
Fahrenheit temperature corresponds to 0 K?