How many pounds of each should be​ used?

Question

The manager of a bulk foods establishment sells a trail mix for $6 per pound and premium cashews for $9 per pound. The manager wishes to make 90 pounds of a trail​ mix-cashew mixture that will sell for $8 per pound.

Answer 1

Let x be trail mix

Let y be premium cashews

so trail mix + premium cashews = 90 pounds

x + y = 90------>Equation 1

now price times trail mix + price times premium cashews = price x 90 pounds

6x + 9y = 8(90)

6x + 9y = 720------>Equation 2

Note: In the above, one has to use the price pertaining to the item it's multiplying with.

Solve the two equations above

x + y = 90

6x+9y = 720

Multiply first equation by 6 throughout

6x + 6y = 540

6x + 9y = 720

- - -

_______________

0 - 3y = - 180

Divide by -3 both sides of equation

y = 60

To find x, one can use either equation 1 or equation 2 above.

In our case we'll use equation 1 as it's simpler to use

x + y = 90

x + 60 = 90

x = 90 - 60

x = 30

The final answer is, there should by 30 pounds of trail mix and 60 pounds of premium cashew.