How many pounds of pineapple and banana chips should be used? (Round your answer to the nearest tenth of a pound.)

Question

A pound of dried pineapple bits sells for $6.29, a pound of dried banana chips sells for $4.69, and a pound of raisins sells for $2.29. Two pounds of raisins are to be mixed with equal amounts of pineapple and banana to create a trail mix that will sell for $4.99 a pound. How many pounds of pineapple and banana chips should be used? (Round your answer to the nearest tenth of a pound.)

Answer 1

We will use 'x' to represent the pounds of both pineapple and banana chips to be used.

Costs:

Pineapple bits: $6.29 per pound

Banana chips: $4.69 per pound

Raisins: $2.29 per pound

Trail mix: $4.99 per pound

The equation for the cost of the trail mix per pound is given by:

2 pounds of raisins at 2.29 per pound: 2(2.29)

which are to be mixed with equal amounts of pineapple and banana: x(6.29+4.69)

Which will sell at 4.99 a pound: 4.99(2+x)

2(2.29)+ x(6.29+4.69)= 4.99(2+x)

Now, let's solve for x:

4.58+x(11.98)= 9.98+4.99x

Combine like terms:

x(11.98−4.99)= 9.98−4.58

6.99x=5.4

x= 5.4/6.99

x≈0.7725

Approximately 0.7725 pounds of pineapple and banana chips should be used. Let me know if you have any questions!