Absolute Value Word Problems

Marcos is cutting ribbons for a craft project. Each ribbon needs to be  $\frac{3}{4}$  yard long and each piece he cuts is plus or minus  $\frac{1}{16}$  yard. Write an equation to find the shortest and longest pieces of ribbon. 

•  $\left|x-\frac{3}{4}\right|=\frac{1}{16}$  

•  $\left|x+\frac{3}{4}\right|=\frac{1}{16}$  

•  $\left|x-\frac{1}{16}\right|=\frac{3}{4}$  

•  $\left|x+\frac{1}{16}\right|=\frac{3}{4}$  

What is the first step? 

• Get absolute value alone by subtracting 5 from both sides
• Get absolute value alone by dividing by 5 on both sides
• Split into two equations

You 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. The number 15 best represents the...

• range

• tolerance

• optimal or average value

• maximum

You are going out in temperatures that are predicted to be 65 degrees plus or minus 5 degrees. Let the actual temperature be T degrees. Which expression represents the difference between the actual temperature and what was predicted?

• 65T

• 65 + T

• T - 65

• | T - 65 |

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

You 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. The number 50 best represents the...

• range

• tolerance

• goal amount (average/optimal amount)

• maximum

The ideal diameter of a piston for a car engine is 88.000 mm. The actual diameter can vary from the ideal diameter by at most 0.007 mm. Find the range of acceptable diameters of the piston.

On average, a squirrel lives to be 6.5 years old. The lifespan of a squirrel may vary by as much as 1.5 years. Write an absolute value equation that could be used to represent maximum and minimum life spans of a squirrel. What are the maximum and minimum ages.

The average January temperature in a northern Canadian city is 1 degree Fahrenheit. The actual January temperature for that city may be about 5 degrees warmer or colder. Write an equation to find the minimum and maximum temperatures.

• |t - 1|=5

• |t - 5|=1

• |t + 1|=5

• |t + 5|=1

A student expects to earn a 93 on her next exam. However, she would be satisfied with a score within 7 points of her prediction. Write an absolute value equation that could be sued to determine the maximum and minimum scores that this student would be happy with.