finding two numbers 15

Question

The sum of two numbers is
114 
If
three times
the smaller number is subtracted from the larger? number, the result is
14.  
Find the two numbers.

Answer 1

Jessica, if we call the smaller number s and the larger number a, then...

 

s + a = 114

a - 3s = 14

 

Hopefully you can see where those equations came from.

 

We can now do different things, but let's solve both equations for a.

 

a = 114 - s

a = 14 + 3s 

 

Hey, if a equals two different things, they must equal each other!

 

114 - s = 14 + 3s

-4s = -100

s = 25

 

Well, if s = 25 and a = 114 - s, then a = 114 - 25 = 89.

 

Boom.