Question

The company sandy shores also packages large bottles of sand. The label on the large bottle of sand states that each bottle contains 40 ounces of sand. The minimum amount of sand allowed in each large bottle is 39.25 ounces. The maximum amount of sand allowed in each large bottle is 40.75 ounces.
A. What is the tolerance , in ounces, that the company allows for the large bottle? Show your explain how you got your answer.

B. Write an Absolute value inequality that represants y, the amount of sand in ounces , that the company Sandy shores allows in the large bottle. Example your reasoning

Answer 1

Answer: A. 0.75 ounces

B. y-40|<0.75, which is the required absolute equation.

Step-by-step explanation:

A. Tolerance = Difference between minimum or maximum value and average value.

Here, minimum value = 39.25 ounces

maximum value = 40.75 ounces

Average = 40 ounces of sand.

Tolerance = 40.75-40= 0.75 ounces

or Tolerance = 40- 39.25= 0.75 ounces

B. Let y = the amount of sand in ounces , that the company Sandy shores allows in the large bottle.

39.25 < y < 40.75

⇒  40-0.75 < y < 40+0.75

⇒  -0.75 < y -40< +0.75  [subtract 40 from all sides]

⇒ |y-40|<0.75, which is the required absolute equation.

For example, length of a wire(l) lies between 2 and 4

So, 2< l < 4

⇒3-1 < l < 3+1

⇒ |l-3|<1