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The coffee counter charges $9 per pound for French roast coffee and $8 per pound for Sumatran coffee. How much of each type of coffee should be used to make 20 L blend that sells for $8.30 a pound?

Respuesta :

Answer: 6 pounds of French roast coffee and 14 pounds of Sumatran coffee was used.

Step-by-step explanation:

Let x represent the number of pounds of French roast coffee that should be added in the blend.

Let y represent the number of pounds of Sumatran coffee that should be added in the blend.

The total number of pounds of the mixture made is 20 lb. This means that

x + y = 20

The mixture sells for $8.30 a pound. The total cost of the mixture would be

8.3 × 20 = 166

This means that

9x + 8y = 166 - - - - - - - - -1

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

9(20 - y) + 8y = 166

180 - 9y + 8y = 166

- 9y + 8y = 166 - 180

- y = - 14

y = 14

x = 20 - y = 20 - 14

x = 6

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