Question

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of​ protein, 2 units of​ carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of​ protein, 1 unit of​ carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of​ protein, at least 11 units of​ carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.

Let x be the number of ounces of fruit and y the number of ounces of nuts. Referring to the​ chart, give the three inequalities that x and y must satisfy because of the​ package's requirements for​ protein, fat, and carbohydrate.

__ _ 8
__ _ 11
__ _ 10

Give the inequalities that x and y must satisfy because they cannot be negative.
y ≥ __
x ≥ __

Answer 1

Explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

Answer 2

Explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0