Question

Write a system of equations (3 points) for the problem below and then solve it The candy shack has 20 lb. Of mixed white and dark chocolate worth $7.50 per pound. White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. How many pounds of each are in the mixture?

Answer 1

Answer: the mixture contained 15 pounds of white chocolate and 5 pounds of dark chocolate.

Step-by-step explanation:

Let x represent the number of pounds of white chocolate in the candy shack mixture.

Let y represent the number of pounds of dark chocolate in the candy shack mixture.

The candy shack has 20 lb of mixed white and dark chocolate. This means that

x + y = 20

The 20lb mixture is worth $7.50 per pound. This means that the total cost of the mixture is

20 × 7.50 = $150

White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. This means that

8x + 6y = 150 - - - - - - - - - - - - - -1

Substituting x = 20 - y into equation 1, it becomes

8(20 - y) + 6y = 150

160 - 8y + 6y = 150

- 8y + 6y = 150 - 160

- 2y = - 10

y = - 10/ - 2

y = 5

x = 20 - y = 20 - 5

x = 15