Question

A grocer wants to make a 10 pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

Answer 1

Answer: 7 pounds of peanuts and 3 pounds of cashew should be used.

Step-by-step explanation:

Let x represent the number of pounds of peanuts that he would use in the mixture.

Let y represent the number of pounds of cashews that he would use in the mixture.

The total mixture would be 10 pounds. It means that

x + y = 10

The mixture of peanuts and cashews would be sold at $4.75 per pound. This means that the total cost of the mixture is

10 × 4.75 = $47.5

If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, it means that

4x + 6.5y = 47.5- - - - - - - - - - - - 1

Substituting x = 10 - y into equation 1, it becomes

4(10 - y) + 6.5y = 47.5

40 - 4y + 6.5y = 47.5

- 4y + 6.5y = 47.5 - 40

2.5y = 7.5

y = 7.5/2.5

y = 3

x = 10 - y = 10 - 3

x = 7