The difference between two numbers is 5, and twice the smaller is 18 more than the larger. Find the numbers.

Question

help i dont know how to do it

Answer 1

Let's call these two numbers x and y, where x is the larger number and y the smaller. The key to these problems is to translate the word problem into a system of equations: 

 

x-y=5

2y=x+18

 

Now, just solve for one of the variables...

 

x=5+y

 

And substitute that variable into the other equation

 

2y=(5+y)+18

 

then solve for the one variable and use that to find the other using either of the original 2 equations.

 

y=23

x=28

 

 

Answer 2

Let x and y be the numbers, with x the larger one.

 

x - y = 5

2y = x + 18

 

Then solve this system of equations:

 

x - y = 5

x - 2y = -18

 

Subtract bottom equation from top equation and get

 

y = 23

 

So x = y + 5 = 23 + 5 = 28