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.

Answer 1

it wold be i mean i think its the 3 one

Answer 2

The correct option are C and E.

Explanation:

Let x be the total weight of the cup in ounces.

It is given that the cup is filled with 4 oz. of yogurt before any toppings are added. So, the initial weight of the cup must greater than or equal to 4.

`x\geq 4` ........(1)

After that toppings are added, they are allowed up to a total weight of 6 oz.

So, the weight of the cup cannot be more that 6

`x\leq 6` ........(2)

On combining (1) and (2). We get

`4\leq x\leq 6`

The acceptable weights for the frozen yogurt is represented by the inequality
`4\leq x\leq 6`.

It means option C is correct and options A, B and D are incorrect.

In option E,

`|x-5|\leq 1`

`-1leq x-5\leq 1`

Add 5 on each sides.

`4 leq x\leq 6`

Option E is correct.

In option F,

`|x-2|\leq 6`

`-6 leq x-2\leq 6`

Add 2 on each sides.

`-4 leq x\leq 8`

Option F is incorrect.

Therefore, the correct options are C and E.