Absolute Functions Word Problems

A company charges $20 for each hour of work up to 5 hours, and $15 for each additional hour. Write a piecewise absolute value function to represent the total cost (y) for x hours of work.

• y = 20x, if x > 5

• y = 15x, if x <= 5

• y = 20x, if x <= 5 y = 20(5) + 15(x-5), if x > 5

• y = 20x + 15, if x <= 5

A car rental company charges $50 per day plus $0.25 per mile driven. Write a piecewise absolute value function to represent the total cost (y) for x miles driven in a day.

• y = 50x + 0.25

• y = 50 - 0.25x

• y = 50 - 0.25/x

• y = 50 + 0.25x

A company charges $15 for each hour of work up to 3 hours, and $10 for each additional hour. Write a piecewise absolute value function to represent the total cost (y) for x hours of work.

• y = $45 + ($10 * (x - 3)) if x > 3 y = $15x if x <= 3

• y = $45 + ($10 * (x - 2)) if x > 3

• y = $15x + $10 if x <= 3

• y = $15 + ($10 * (x - 3)) if x > 3

A company charges $10 for each hour of work. Write an absolute value function to represent the total cost (y) for x hours of work.

• y = 10|x|

• |y| = |10x|

• |y| = 10x

• y = -10x

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x-50|=15

• |x+15|=50

• |50+x|=15

• No Solution

The street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within the tolerated widths must be repaired. Which of the following inequalities can be used to assess which streets are within tolerance? (W is the width of the street) .

• |W - 25| ≤ .5

• |W - .5| ≤ 25

• |W - 25| ≥ .5

• |W - .5| ≥ 25

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03

• |v-20|=0.03

• |v|-0.03=20

• |v-0.03|=20

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1

• |x – 6| ≥ 0.1

• |x – 0.1| ≤ 6

• |x – 0.1| ≥ 6

A candy manufacture puts 240 pieces of candy into each bag. The bag can be off by 8 pieces. Write an absolute value inequality that displays the acceptable amount of candy pieces that can be in a bag.

A factory produces bolts that must be 5 inches in length with a tolerance of 0.2 inches. Bolts that are not within the tolerated lengths will be discarded. Which of the following inequalities can be used to assess which bolts are acceptable? (b is the length of the bolt)

• |b - 5| ≤ 0.2

• |b - 5| ≥ 0.2

• |b - 0.2| ≤ 5

• |b - 0.2| ≥ 5