Question

A grocer sells milk chocolate at $2.90 per pound, dark chocolate at $4.90 per pound, and dark chocolate with almonds at $5.50 per pound. He wants to make a mixture of 50 pounds of mixed chocolates to sell at $4.80 per pound. The mixture is to contain as many pounds of dark chocolate with almonds as milk chocolate and dark chocolate combined. How many pounds of each type must he use in this mixture?

Answer 1

Answer: milk chocolate = 10 pounds

Dark chocolate =15 pounds

Dark chocolate with almonds = 25 pounds.

Explanation:

What we have here is a proportion problem.

Milk chocolate = $2.90

Dark chocolate = $4.90

Dark chocolate with almonds = $5.50

We are to have 50 pounds of mixed chocolate

Amount the grocer makes from this

= $4.80 × 50 = $240

However, we must consider how much the grocer would have made if he had sold them separately

Weight of milk chocolate = x

Weight of dark chocolate = y

Weight of dark chocolate with almond = z

x+y = z (according to the question)

x+y+z= 50

Equating the collective amount of each type of chocolate with the amount they all cost together

2.90x + 4.90y + 5.50z = 50(4.80)

2.90x + 4.90y + 5.50z = $240

But z = x + y

2.90x + 4.90y + 5.50 (x+y) = $240

2.90x + 4.90y + 5.50x + 5.50y = 240

8.40x + 10.40y = 240 .....eqn 1

Since x + y + z = 50

x + y = 50 - z

But x+ y = z

x + y = 50 - (x+y)

x + y = 50 - x - y

2x + 2y = 50

(Divide through by 2)

x+y = 25 ...... Eqn 2

y = 25 - x

Substitute for y in eqn2

8.4x + 10.4 (25-x) = 240

8.4x + 260 - 10.4x = 240

8.4x - 10.4x = 240 - 260

-2x = -20

x = 10 pounds

y = 25-x

y = 25-10

y=15pounds

x+y+z= 50

10+15+z= 50

25+z=50

z= 50-25

z = 25