a number minus a number equals 18 the two numbers together equal 33 how to find both numbers

Question

if you have a number minus a number equals 18 and both of those numbers equal 33 how do I find the two numbers

Answer 1

Our first step here would be to set up equations for both of these pieces of information

x - y = 18 and x + y = 32

Next we need to solve for one of the variables in terms of the other one. I will be solving for x, but either way is fine. To do this, I am adding y to both sides of the first equation to isolate x, which gives me

x = 18 + y

Now that we have a value for x that is in terms of y, we can substitute this into the second equation

18 + y + y = 32

Combining like terms gives us

18 + 2y = 32

Subtracting 18 from both sides, we get

2y = 14

And dividing by 2 solves for y

y = 7

With this information, we can now plug that value of y into the first equation to get

x - 7 = 18

Adding 7 to both sides, we see that

x = 25

The two numbers are 25 and 7