The difference of two numbers is 18. Three times the smaller minus the larger is -12. Find the numbers.

Answer 1

Hi, Spencer,

Let S be the small number, and L be the large. We are told that their difference is 18. Since this is a positive number, we can use the equation L - S = 18. (The S is subtracted: allowing the result to be positive.)

We are also told that three times the smaller (S) minus the larger (L) is -12.

Writing this as an equation, we get

3S - L = -12, or rewriting it,

L = 12 +3S

We have two equations, so let's find a way to eliminate one of the two variables (S or L). Looking at the first equation, I think I'd like to rearrange it so that we have L on the left and the rest on the right:

L = S + 18

Aha, Now I can use this definition of L to plug in the second expression:

L = 12 +3S

S + 18 = 12 + 3S

-2S = -6

S = 3

If S = 3, and L - S is 18, L must be 21

Check the results:

L - S = 18

21 - 3 = 18 Checks

3S - L = -12

3*3 - 21 = 9 - 21 = -12 Checks

I hope this helps,

Bob

Answer 2

numbers: x, y

| x - y | = 18

Let's say x is bigger, so we can simplify to x - y = 18.

Three times the smaller minus the larger is negative 12

3y - x = -12

Let's solve both equations for x.

The first becomes: x = y + 18.

The second becomes: x = 3y + 12.

Now let's set them equal to each other.

y + 18 = 3y + 12.

Let's solve for y.

2y = 6

y = 3

Now we can plug y into the original equation.

x - y = 18 -> x - 3 = 18

If we solve for x, we get x = 21.

Therefore, the numbers are 21 and 3.

Let's plug them in to check.

21 - 3 = 18: good

3*3 - 21 = -12 -> 9 - 21 = 12: good

We have now confirmed that our two numbers are 21 and 3.