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# i need help figuring out how to work this problem

three times a number minus two times another number equals 19. The sum of the two number is 18. find the two numbers

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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Three times a number minus two times another number equals 19. The sum of the two number is 18. find the two numbers

Let m = one of the numbers and n = the other number

We have two unknowns (n and m), so we need two equations relating them to find the solution.

Equation 1 - Three times a number minus two times another number equals 19

3m - 2n = 19

Equation 2 - The sum of the two numbers is 18

m + n = 18

We can re-write this equation as:

n = 18 - m

Now let's substitute 18-m in place of n in Equation 1:

3m - 2n = 19             (equation 1)

3m - 2(18-m) = 19     (Substitute 18-m in place of n)

3m - 36 +2m = 19     (Multiply out the parentheses)

5m = 55                    (Add the m terms, add 36 to both sides)

Solve for m, then use n = 18 - m to solve for n.  Check your answers by putting them into equation 1 and verifying that they produce 19 for the answer.