Expert: Sherry Wallin - 1/24/2009

Question
Hello:

I saw a furniture store commercial in which the salesman indicated that the furniture was on sale at 59 cents on the dollar.

Does 59 cents on the dollar indicate that for every dollar that the piece of furniture cost, just replace the dollar amount, $200 with $0.59, 200 times?

For example if a chair cost $200.00 the actual cost would be ($0.59)/($1.00) X $200 = $118. So the price for the chair would be $118. Or another way to think of it as adding $0.59, 200 times. This would be the same as I indicated above: $0.59)/($1.00) X $200 = $118.

And also, I am assuming that 59 cents on the dollar represents $0.59 per dollar or ($0.59)/($1.00).

Suppose I want to determine the amount on the dollar if I didn't know it.
Would this calculation be logical: (?)/$1.00 X $200 = $118.  Now divide $118 X $1.00 by $200 or ($118 X $1.00)/$200 = $0.59.

I thank you for your reply and assistance regarding my question.

Answer
Hi Kenneth~
    Everything you said perfectly. For $.59 on the dollar is exactly for every $ in cost you will only pay 59 cents. So knowing that, you would just multiply .59 times the amount it was originally selling for. Another way to think of it is that you are getting a 41% discount. There are a couple of ways to do this kind of problem. First you need to know that 59% and 41% are complements of each other because they add up to 100% = 1. .59 and .41 are complements of each other because they add up to 1. When you get a discount of say 25% it is really the price times the complement, meaning the price times 75%. This is equivalent to finding 25% of the price and then subtracting it from the price to get the sale price. So back to your problem and your question:

"Suppose I want to determine the amount on the dollar if I didn't know it.
Would this calculation be logical: (?)/$1.00 X $200 = $118.  Now divide $118 X $1.00 by $200 or ($118 X $1.00)/$200 = $0.59".

Since a dollar is 1 why not just let x = amount on the dollar and then use 200x = 118 and to solve for x just divide both sides by 200.

Hope this helps a bit.

Math Prof