Question

8. Willie wanted to create chocolate milk using whole

milk and chocolate syrup. He wanted his chocolate
milk to have less than 8 grams of fat and less than 28
grams of sugar. He created two mixtures. The focus of
the first mixture was on the amount of fat. He
combined x ounces of whole milk containing 1 gram of
fat per ounce with y ounces of chocolate syrup
containing 0.32 grams of fat per ounce. The second
mixture was focused on sugar and consisted of x
ounces of whole milk containing 1.5 grams of sugar per
ounce and y ounces of chocolate syrup containing 14
grams of sugar per ounce.
a. Write a system of inequalities to represent the
constraints of this situation.
b. Which of the following would be viable
combinations of milk and chocolate syrup
based on Wille's constraints?
A. 0 ounces of milk and 2 ounces of chocolate syrup
B. 3.5 ounces of milk and 3.5 ounces of chocolate
syrup
C. 2.25 ounces of milk and 1.5 ounces of chocolate
syrup
D. 8 ounces of milk and 0 ounces of chocolate syrup

Answer 1

a. The system of inequalities can be written as: x + 0.32y ≤ 8 (constraint for fat) and 1.5x + 14y ≤ 28 (constraint for sugar). b. The viable combinations of milk and chocolate syrup based on Willie's constraints are A, B, C, and D.

a. The system of inequalities can be written as:

x + 0.32y ≤ 8 (constraint for fat)

1.5x + 14y ≤ 28 (constraint for sugar)

b. We can substitute the given answer choices into the inequalities and check if they satisfy the constraints:
A. x=0, y=2 - Substituting these values in the inequalities, we get:
0 + 0.32(2) ≤ 8 ⇒ 0.64 ≤ 8 (True)
1.5(0) + 14(2) ≤ 28 ⇒ 28 ≤ 28 (True)
Therefore, A is a viable combination.
B. x=3.5, y=3.5 - Substituting these values in the inequalities, we get:
3.5 + 0.32(3.5) ≤ 8 ⇒ 4.92 ≤ 8 (True)
1.5(3.5) + 14(3.5) ≤ 28 ⇒ 28 ≤ 28 (True)
Therefore, B is a viable combination.
C. x=2.25, y=1.5 - Substituting these values in the inequalities, we get:
2.25 + 0.32(1.5) ≤ 8 ⇒ 2.94 ≤ 8 (True)
1.5(2.25) + 14(1.5) ≤ 28 ⇒ 26.25 ≤ 28 (True)
Therefore, C is a viable combination.
D. x=8, y=0 - Substituting these values in the inequalities, we get:
8 + 0.32(0) ≤ 8 ⇒ 8 ≤ 8 (True)
1.5(8) + 14(0) ≤ 28 ⇒ 0 ≤ 28 (True)
Therefore, D is a viable combination.
Hence, the viable combinations of milk and chocolate syrup based on Willie's constraints are A, B, C, and D.