Question

Eduardo mixed 5 pounds o cashews and almonds. Cashews cost $8 per pound and almonds cost $6 per pound. The total cost of the mixture was $33. How much of the mixture was almonds?

Answer 1

3.5 pounds of the mixture was almonds

Explanation:

Assume that the mixture contains x pounds of cashews and y pounds of almonds

∵ x represents the amount of cashew

∵ y represents the amount of almond

∵ Eduardo mixed 5 pounds of cashews and almonds

∴ x + y = 5 ⇒ (1)

∵ Cashews cost $8 per pound

∵ Almonds cost $6 per pound

∵ The total cost of the mixture was $33

→ Multiply x by 8 and y by 6 and equate their sum by 33

∴ 8x + 6y = 33 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by -8 to eliminate x

∵ -8(x) + -8(y) = -8(5)

∴ -8x - 8y = -40 ⇒ (3)

→ Add equations(2) and (3)

∵ (8x + -8x) + (6y + -8y) = (33 + -40)

∴ -2y = -7

→ Divide both sides by -2

∴ y = 3.5

∵ y represents the amount of almond

∴ 3.5 pounds of the mixture was almonds