The sum of two numbers is 15. Four times one of the numbers is twelve more than two times the other number. What are the two numbers?

Let a and b be our two numbers.

Here is the set up:

a + b = 15 ... A

4a = 2b + 12 ... B

We have a system of equations in two variables.

Solve equation A for either a or b. I decided to solve for a.

a + b = 15

a = 15 - b

Plug into equation B.

4 (15 - b) = 2b + 12

Solve for b.

60 - 4b = 2b + 12

-4b - 2b = 12 - 60

-6b = - 12

b = - 12/-6

b = 2

We now know that b is 2. To find a, plug b = 2 into either equation A or B.

As you can see, equation A is easier to deal with.

a + b = 15

a + 2 = 15

a = 15 - 2

a = 13

The two missing numbers are 2 and 13.