How many different ways can she purchase candy?

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Question from fathia, a parent:

Hi,

Could you please help me with this question ?

Stephanie can buy lemon candies for 3 cents each and chocolate candies for 5 cents each. Stephanie has 64 cents to spend. How many different ways can she purchase candy if she wants to spend all her money?

Hi Fathia.

This is a question concerning whole numbers.

Let L = the number of lemon candies and C = the number of chocolate candies.

Then 3L + 5C = 64.

If Stephanie bought all the chocolate candies she could, she'd buy 12 chocolates because that costs 60 cents (12 x 5 = 60) and 13 would cost more than she has. So you know that the answer is 12 or less.

That is a small enough number just to experiment, but you can see a method if you notice that the cash left over after she buys chocolate candies must be an even multiple of 3 cents. Can you see a pattern?

Stephen La Rocque.>

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.