Question

Celia bought 12 apples, ate two of them, and sold the rest at 20 cents more per apple than she paid. Her total profit was $1.00. How much did she sell each apple for?

Answer 1

Celia sold each apple for 70 cents.

Explanation:

So, we have 10 apples sold at price `x`, so that is `10*x` and 12 apples bought for 20 cents less than that price `x`, so that is `12*(x-0.20)`.

Now we have to make an equation where these sides equal each other. We know that the sale total of the 10 apples is 1 dollar more than the purchase price of the 12 apples so:
`12*(x-0.20)+1=10*x`

Then we solve for `x`, like so:
1) Multiply the number outside the parentheses by each of the terms inside the parentheses
`" "12*x-12*0.20+1=10*x`
`" "12*x-2.40+1=10*x`
`" "12*x-1.40=10*x`

2) Add 1.40 to both sides:
`" "12*x-1.40+1.40=10*x+1.40`
`" "12*x-cancel(1.40+1.40)=10*x+1.40`
`" "12*x=10*x+1.40`

3) Subtract `10*x` from both sides:
`" "12*x-10*x=10*x-10*x+1.40`
`" "2*x=cancel(10*x-10*x)+1.40`
`" "2*x=1.40`

4) Divide each side by 2:
`" "(2*x)/2=1.40/2`
`" "(cancel(2)*x)/cancel2=0.70`
`" "x=0.70`