Question

You manage I Dream of Ice Cream, an ice cream factory that specializes in 3 fla- vors: Vanilla, Chocolate, and Mint. Into each batch of Vanilla go 2 eggs and 1.5 cups of milk. Into each batch of Chocolate go 3 eggs and 1 cup of milk. Into each batch of Mint go 1 egg and 2 cups of milk. You want to use all of your stock of 100 eggs and 60 cups of milk. Also, Chocolate is more popular than Vanilla and Mint, so you make the same amount of Chocolate as the other two combined. Set-up, but do not solve, a system of equations that completely describes this situation. Use variables V, C,

Answer 1

The correct answers are as follows

2 × a + 1.5 × b = V.

1 × c + 2 × d = M.

3 × h + 1 × k = C = V + M.

a + c + h = 100.

b + d + k = 60.

Explanation:

I Dream of Ice Cream, an ice cream factory that specializes in 3 flavors: Vanilla (V) , Chocolate (C) , and Mint (M).

Let I Dream of Ice Cream makes V amount of Vanilla flavored ice cream.

Let I Dream of Ice Cream makes M amount of Mint flavored ice cream.

Let I Dream of Ice Cream makes C ( = V + M ) amount of Chocolate flavored ice cream as chocolate is more popular than the other two.

Into each batch of Vanilla go 2 eggs and 1.5 cups of milk. Let a eggs and b cups of milk are added to make vanilla ice cream.

∴ 2 × a + 1.5 × b = V.

Into each batch of Mint go 1 egg and 2 cups of milk. Let c eggs and d cups of milk are added to make mint ice cream.

∴ 1 × c + 2 × d = M.

Into each batch of Chocolate go 3 eggs and 1 cup of milk. Let h eggs and k cups of milk are added to make mint ice cream.

∴ 3 × h + 1 × k = C = V + M.

In order to use all of the stock of 100 eggs and 60 cups of milk,

a + c + h = 100.

b + d + k = 60.