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

Answer:

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.

If you want to learn more about inequalities, you can read:

From the answer and question examples above, hopefully, they could simply guide the student answer the question they had been looking for and keep in mind of all the stuff stated in the answer above. Then could possibly make some sharing in a group discussion and also learning with the classmate about the topic, so another student also procure some enlightenment and still keeps up the school learning.

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