The difference between two numbers is 9. The first number plus twice the other number is 27. Find the two numbers

Answer 1

In order to solve this, we can turn each sentence into its own equation. Lets call the first number x and the other number y.

The difference between the two numbers is 9, so that gives us:

x - y = 9

And the first number plus twice the other number is 27, so that gives us:

x + 2y = 27

Now we have a system of two equations and we can use elimination to get rid of x. If you notice, both equations have just one x in them, so if we subtract the first equation from the second one the x terms will cancel out:

(x + 2y) - (x - y) = 27 - 9

3y = 18

Now we can divide by 3 on both sides to solve for y:

y = 6

Now that we have the value of y, we can plug it back into the first equation to find x:

x - 6 = 9

x = 15

You can always check your answer by putting both numbers back into the original sentences. The difference between 15 and 6 is 9, and 15 plus twice 6 is 15 + 12 which is 27, so both of them work.

So, our final answer is 15 and 6.

Answer 2

Here's what we know:

x - y = 9 (the difference between the two is 9)

x + 2y = 27 (the first plus twice the second is 27)

We can use the elimination method here. By multiplying the first equation by -1 and then tetal the two equations together, we can remove x and find y:

-x + y = -9

x + 2y = 27

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3y = 18

Divide by 3:

3y / 3 = 18 / 3

y = 6

Now that you know y, you can find x by placing it into each equation. (One to solve, the other to check your work)