find two numbers with sum of 21 and difference is 10

Question

Find two numbers with sum of 21 and difference is 10

Answer 1

Hi, Katherine,

 

First, let's define the two numbers with variables. Let x be the first number and y be the second number. So the sum of the two numbers is 21, so you have to add the two variables: x + y = 21. It also says the difference is 10, so x-y = 10. So it looks like you have a system of 2 equations and 2 unknowns.

 

x+y = 21

x-y = 10

 

You can use either substitution method or elimination method. If you use elimination method, you would have to add the two equations to cancel out the y's. 

 

         x+y = 21

 (+)  x - y = 10

_________________

 

     2x  + 0 = 31   because x + x = 2x, and y + (-y) = 0

 

    2x = 31, then divide both sides by 2

 

x = 31/2, so this is your first number

 

Now, you can plug this into any of the equations on top. Let's plug x = 31/2   into x + y = 21:

 

31/2 + y = 21;  subtract 31/2 on both sides

 

y = 21-31/2  = 11/2 

 

So your two numbers are 31/2 and 11/2  (which is the same thing as 15.5 and 5.5)

 

Hope this helps :)

 

Emmanuel