I have enough money to buy five regular CD's and have $6 left over. However, all the CD's are on sale today, for $4 less than usual. If i borrow $2, I can afford nine of them. How much are CD's on sale for today?

You want to know the sale price of CDs if I can buy 5 at regular price and have 6 dollars left over, but I need to borrow 2 dollars to buy 9 at the sale price of 4 dollars off.

Setup

Let s represent the sale price of a CD. Then (s+4) is the regular price. The amount of money I have in each case can be described by ...

5(s+4) +6 = 9s -2

Solution

Simplifying the equation gives ...

5s +26 = 9s -2 . . . . . . . . eliminate parentheses, combine terms

28 = 4s . . . . . . . . . . . . add 2-5s to both sides

7 = s . . . . . . . . . . . . . divide by 4

The sale price of a CD is 7 dollars.

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Additional comment

We could have found the regular price, then subtracted 4 dollars to get the sale price. Often, it is convenient to solve directly for the value the problem is requesting. That way, the solution to the equation is the answer to the question, with no additional steps required.