Setting up equation to solve a word problem

Question

Natasha is 9 times Eric's age. In 10 years, the sum of their ages will be 50. What is Natasha's age now? Can you please explain how I would set up this equation...thank you 

Answer 1

First thing to do with any word problem is to define the terms. In this case let's say:

Natasha's age=N

Eric's age=E

 

Now let's figure our what we know and try to make them into equations:

 

Natasha's age is 9 times Eric's age. In other words:

N=9xE

 

In 10 years, the sum of their ages will be 50. This one is a little bit tricky. We have to remember to add 10 years to both Natasha's and Eric's ages (since they have both aged 10 years), then add them together and let that equal 50. Looks like this:

N+10+E+10=50

or

N+E+20=50

 

Now we can do something really useful! Since we know that N=9xE we can remove one of the letters in the equation. This allows us to solve for the other letter!

 

N+E+20=50

becomes:

9xE+E+20=50

 

Now you can solve for E and then solve for N using the equation N=9xE.