a first number plus twice a second number is 15. twice the first number plus the second totals 12. find the numbers

Answer 1

Hi, Emily.

Okay, let's call the first number, N and the 2nd number M.

Now we have 2 equations.

N + 2M = 15

2N + M = 12

Now, from the first equation we can solve for N

N + 2M = 15

N + 2M - 2M = 15 - 2M

N = 15 - 2M

So now we can substitute that value of N into the 2nd equation:

2N + M = 12

2(15 - 2M) + M = 12

30 - 4M + M = 12

30 - 3M = 12

30 - 3M + 3M = 12 + 3M

30 - 12 = 12 - 12 + 3M

18 = 3M

M = 18/3 = 6

Now, if M = 6, substitute into the first equation to get the value of N.

N + 2M = 15

N + 2(6) = 15

N + 12 = 15

N = 3

So, now we can check the 2nd equation to make sure the answer is right:

2N + M = 12

2(3) + 6 = 12

6 + 6 = 12

Therefore, the answers are 3 and 6