Question

Sam bought some apples by the pound. He sold half the apples for $50\%$ more per pound than his purchase price. He then sold half of the remaining apples for $25\%$ more per pound than his purchase price. He then sold the remaining 650 pounds of apples for $25\%$ less per pound than his purchase price. If he had $\$2600$ in total sales, what was Sam's purchase price, in cents per pound, for the apples?

Answer 1

80 cents

Explanation:

After selling half of his apples twice 1/4 remain, meaning that in total he bought 2600 pounds of apples.

Lets take the purchase price to be D

He sold the first half which is 1300 for 1.5D =1300(1.5D)

He sold the second half which is 650 for 1.25D =650(1.25D)

and the last half which is also 650 for 0.75D = 650(0.75D)

Representing this in an equation gives you:

2600=1300(1.5D)+650(1.25D)+650(0.75D)

Since he made 2600 dollars in total

Simplify both sides by 2600, you get this:

1=3/4D +5/16D +3/16D

solve it to get 4/5D

4/5 of a dollar gives you 80 cents.