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Lucy has to make a chocolate candy mixture. She needs to have 13 pounds that sell for 7$ a pound. She has two types available, a heart shaped chocolate that sells for 4$ a pound and rose shaped chocolate that sells for 8.50$ a pound. How much of each type does she need to use

Respuesta :

Answer: she needs to use 4.3 pound of heart shaped chocolate and 8.7 pound of rose shaped chocolate.

Step-by-step explanation:

Let x represent the number of pounds of heart shaped chocolate that she needs to use.

Let y represent the number of pounds of rose shaped chocolate that she needs to use.

She needs to have 13 pounds that sell for 7$ a pound. This means that

x + y = 13

The total cost of 13 pounds of the mixture would be

13 × 7 = $91

She has two types available, a heart shaped chocolate that sells for 4$ a pound and rose shaped chocolate that sells for 8.50$ a pound. This means that

4x + 8.5y = 91 - - - - - - - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

4(13 - y) + 8.5y = 91

52 - 4y + 8.5y = 91

- 4y + 8.5y = 91 - 52

4.5y = 39

y = 39/4.5 = 8.7 pounds

x = 13 - y = 13 - 8.7

x = 4.3

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