Name: Valerie
Level: middle school student

At a discount T-shirt shop the manager marked a special batch of T-shirts that originally sold for $2.00. When all the shirts sold the shop had collected $603.77.

How many shirts did they sell and what was the price per shirt?

Hi Valerie,

The amount of money collected is $603.77, which is the product of the discount price and the number of T-horts sold. If you express the discount price and the amount of money collected in cents rather than dollars then you have 60377 as the product of two integers, the discount price in cents and the number sold.
   Start by writing a list of integers starting at 200, 199, 198, ...150. These are the possiblities for the discount price in cents. (I am assuming that the discount price won't be less than $1.50. If this doesn't work you will have to extend the list.) Since the discount price times the number sold is 30677, and 30677 is odd, the discount price is also odd, so stroke out all the even numbers in your list. 60377 is also not divisible by 3 hence the price is not divisible by 3 so strike out all the multiples of 3 from your list. Again 30677 is not divisible by 5 hence the price is not divisible by 5 so strike out all the multiples of 5 from your list. Your list now should look like 199, 197, 193, ...
   Now it's calculator time. Divide 30677 by the remaining numbers in your list until you get a division with no remainder. The number that you successfully divided by will be the price in cents, and the quotient (the answer) will be the number of T-shirts sold.

I hope that this helps.
Jack and Penny