Question

Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound, and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?

Answer 1

3 pounds of peanuts and 2 pounds of cashews

Explanation:

Let x be the pounds of peanuts and y be the pounds of cashews

Greta wants to make 5 pounds of a nut mix using peanuts and cashews.

So,
`x+y=5` ----- A

Cost of 1 pound of peanuts = $4

Cost of x pounds of peanuts = 4x

Cost of 1 pound of cashews = $9

Cost of y pounds of cashews = 9y

Her budget requires the mixture to cost her $6 per pound

So, cost of mixture of x pounds of peanuts and y pounds of cashews is 6(x+y)

So,
`4x+9y=6(x+y)` --- B

Plot A and B

`x+y=5` ---Blue

`4x+9x=6(x+y)` ---Green

Refer the attached figure

Intersection point = (x,y)=(3,2)

Hence she should use 3 pounds of peanuts and 2 pounds of cashews