Juan is thinking of two numbers. he says that 3 times the first number minus the second number is 118. in addition, two times the first number plus the second number is 147. find the numbers.

We will call the first number n, and the second number x.

3n-x=118

2n+x=147

Now, solve one of the equations for x.

x=147-2n

Then, substitute this into the other formula for x. 

3n-(147-2n)=118

Next, solve for n:

3n-147+2n=118
5n=265
n=53
^^^That's your first number.

Lastly, plug in 53 for n into either equation to solve for x.

2(53)+x=147
106+x=147
x=41
^^^This is your second number.