# At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:

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## Question:

At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:

A.) 0 < x ≤ 6 B.) 0 < x ≤ 3 C.) 4 ≤ x ≤ 6 D.) x ≤ 6 E.) |x - 5| ≤ 1 F.) |x - 2| ≤ 6

By writing an inequality and then converting it to an absolute value equation, we will see that the correct options are C and E.

### How to find an inequality?

To find the inequality, we need to find the lower and upper bounds.

First, we know that the machine fills the cups with 4 oz of yogurt, so this is the minimum value allowed, we will have:

4 ≤ x

Then we can add toppings to a maximum value of 6 ounces, this will be the maximum, then we have:

4 ≤ x ≤ 6

We can also write this an absolute value equation, we define:

• m = half of the difference of the bounds.
• M = lower bound + m
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Then the absolute value equation is:

|x – M| ≤ m

By replacing what we found before, we have:

• m = (6 – 4)/2 = 1
• M = 4 + 1 = 5

So the absolute value equation is:

|x – 5| ≤ 1

Finally, we can conclude that the correct options are C and E.