Absolute Value Application Problems
Name: ________________________________________
1. Sarah has $15. She knows that Blake has some money and it varies by at most $5 from the amount of her
money.
a. Write an absolute value inequality that represents this scenario.
b. What are the possible amounts of money that Blake can have?
2. A company is making mirrors. Each mirror needs to be 18 inches high. Each mirror can vary by at most
0.01 of an inch.
a. Write an absolute value inequality that represents the situation.
b. What are the acceptable heights of this company’s mirrors?
c. What are the unacceptable heights of this company’s mirrors?
3. The weather forecast for today states that the average temperature is going to be 55°𝐹 and the
temperature is going to vary by at most 8°𝐹.
a. Write an absolute value inequality that represents the scenario.
b. What are the possible temperatures for today?
4. A musical group’s new single is released. Weekly sales s (in thousands) increase steadily for a while and
then decrease as given by the function 𝑠 = −2|𝑡 − 20| + 40 where t is the time
(in weeks).
a. Graph the function.
b. What was the maximum number of singles sold in one week?
5. A company sells bags of oranges. Each bag of oranges should weigh 8.5 pounds. Each bag can vary by at
most 1.5 pounds. The company ships their oranges with 10 bags of oranges to a box.
a. Write an absolute value inequality that represents the scenario.
b. What are the unacceptable weights of 1 box of oranges?
6. While playing pool, you try to shoot the eight ball into the corner pocket as shown. Imagine that a
5
coordinate plane is placed over the pool table. The eight ball is at (5, ) and the pocket you are aiming for is
4
at (10, 5). You are going to bank the ball off the side at (6,0).
a. Write an equation for the path of the ball.
b. How far does the ball travel before falling into the pocket?
7. A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in
inches per hour) at which it rains is given by the function 𝑟 = −0.5|𝑡 − 1| + 0.5 where t is the time (in
hours).
a. Graph the function.
b. For how long does it rain and when does it rain the hardest?
c. The total amount of rain that falls during the rainstorm can be determined by the area in the first
quadrant in between the graph and the x-axis. How much rain fell during the storm?
8. Suppose a musical piece calls for an orchestra to start at fortissimo (about 90 decibels), decrease in
loudness to pianissimo (about 50 decibels) in four measures, then increase back to fortissimo in another
four measures. The sound level s (in decibels) of the musical piece can be modeled by the function
𝑠 = 10|𝑚 − 4| + 50 where m is the number of measures.
a. Graph the function for 0 ≤ 𝑚 ≤ 8.
b. For which measures, 0 ≤ 𝑚 ≤ 8, will the orchestra be at or below the loudness of mezzo forte
(about 70 decibels)?
9. You are trying to make a hole-in-one on the miniature golf green shown. Imagine that a coordinate plane is
placed over the golf green. The golf ball is at (2.5,2) and the hole is at (9,2). You
are going to bank the ball off the side wall of the green at (6,8).
a. Write an equation for the path of the ball.
b. Will you make your shot?
c. At what angle does the golf ball bounce off of the wall? (Use trig)
10. The Transamerica Pyramid, shown at the right, is an office building in San Francisco. It
stands 853 feet tall and is 145 feet wide at its base. Imagine that a coordinate plane is
placed over a side of the building. In the coordinate plane, each unit represents one foot,
and the origin is at the center of the building’s base.
a. Write an absolute value function whose graph is the v-shaped outline of the sides of
the building, ignoring the “shoulders” of the building.