Question

Gary is baking pretzels for his sister's party. Some pretzels will be regular and some pretzels will be whole grain. Let x represent the number of dozens of regular pretzels. Let y represent the number of dozens of whole grain pretzels. Gary needs to bake at least 14 dozen pretzels in all. Gary has 20 cups of flour. He needs 2 cups of flour for each batch of 12 whole grain pretzels, and 1 cup of flour for each batch of 12 regular pretzels.

Select the constraints that correctly model the inequality.

x≤0

x≥0

y≤0

y≥0

x+2y≤20

x+2y≥20

x+y≥14

Answer 1

the correct answer is
`x + y \geq 14` and
`x + 2y \leq 20`

Explanation:

A dozen of anything mean 12 of anything.Number of regular pretzels are equal to 12x and the total number of whole grain pretzels are equal to 12y.So therefore the total number of pretzels are given by
`12x + 12y` , which can be equal or greater than 14 dozen (14x12) pretzels, which leads us to the first part of the first inequality given by,

`12x + 12y \geq 14*12`

dividing the above inequality by 12 we obtain our first inequality in its reduced form that is,

`x + y \geq 14`

Now moving on to the next part of the question. 2y cups of flour are required for whole grain pretzels and x cups of flour are required for regular pretzels. The total number of flour cups are equal to
`2y + x` , but according to the second part of this question they should be either less than or equal to 20 cups, because we don't have available more than 20 flour cups. This gives us our second inequality,

`x+ 2y \leq 20`.