linear equations

Question

Bob buys Halloween candy. Some pieces cost 2¢ each and some cost 5¢ each. There are 7
more of the 2¢ pieces. The total cost was $1.54. How many 5¢ pieces were purchased?

Answer 1

Hi Blake!

 

So the first thing you want to do when you get a question like this is to ask yourself what you are looking for. Here, you are looking for the number of 5 cent candies. 

 

The second step is asking yourself how many unknown variables you have: you have 2: the 2 cent candies and 5 cent candies. 

 

If you have two unknown variables, you ALWAYS need two equations. 

 

What will your two equations be? First step - assign variables. I prefer X and Y but they can be anything.

 

X = 2 cent candy

Y = 5 cent candy

 

We have the total cost of all the candies - 154 cents. It has to be the sum of the candies.

 

EQUATION 1: 154 = 2X + 5Y

 

How we have to have another equation. We know that there are 7 more of the 2 cent candies that the 5 cent candies.

 

EQUATION 2: X = Y + 7

 

You have the two equations. 

 

154 = 2 (Y + 7) + 5Y

 

Solve for Y! which is the 5 cent candy!