Question

PLSS HELP ASAPPPPP!!!

A plant produces sport drinks, which must be within 0.45 fluid ounces of the advertised 20 fluid ounces on the label. If x represents the volume, write an equation to model the maximum and minimum volumes and determine the minimum volume in a bottle.

|x − 0.45| = 20; x = 19.55 ounces

|x + 0.45| = 20; x = 20.45 ounces

|x − 20| = 0.45; x = 19.55 ounces

|x + 20| = 0.45; x = 20.45 ounces

Answer 1

C

Step-by-step explanation:

Answer 2

Answer: Choice C

Equation is |x − 20| = 0.45

The min is x = 19.55

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Step-by-step explanation:

fl oz = fluid ounces

x = volume of the drink in fl oz

The expression |x-20| represents how far x is from the target of 20 fl oz. We use absolute value to ensure the result is never negative. It might help to draw out a number line.

Two examples:

• If x = 22 then |x-20| = |22-20| = |2| = 2 which shows that 22 is 2 units away from 20 on the number line.
• If x = 17 then |x-20| = |17-20| = |-3| = 3 which shows that 17 is 3 units away from 20 on the number line.

We want this difference to be within 0.45 fl oz, i.e. we want |x-20| to either equal 0.45 or be smaller than it.

If we only cared about the min and max, then we set |x-20| equal to 0.45 to generate the equation |x − 20| = 0.45

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Solve this equation to find the min and max.

|x - 20| = 0.45

x-20 = 0.45 or x-20 = -0.45

x = 0.45+20 or x = -0.45+20

x = 20.45 or x = 19.55

The min is 19.55 fl oz and the max is 20.45 fl oz.

Phrased another way: the x values span from 19.55 to 20.45, inclusive of both endpoints. We could write
`19.55 \le \text{x} \le 20.45` as a compact way to describe what values x could be.