girls outnumber boys by 170 at a recent math symposium. if the ratio of girls to boys was 7:5, how many students attend the symposium?

Question

Thank you for your help.

Answer 1

As always, the first step is to set up the variables:

 

Let x = the number of boys

 

Then the number of girls is x + 170

 

So the ratio of girls to boys, (x+170) / x is equal to 7/5.

 

That gives us an equation:  (x+170)/x = 7/5

 

Let's solve it:

 

multiply both sides by x:

x+170 = 7x/5

 

subtract x from both sides:

170 = 7x/5 - x = 7x/5 - 5x/5 = 2x/5

 

Divide both sides by 2/5

 

170 / (2/5) = x

425 = x

 

So the number of boys is 425 and therefore the number of girls is 425+170 = 595.

 

So the total number of students was 425 + 595 = 1020.

 

Let's check by finding the ratio of girls to boys:

 

Does 595/425 = 7/5?  Prove that to yourself and you will see that the answer is correct.