The difference of two timber's is 8. When twice the first number is added to three times the second number, the result is 51. What are the two numbers?

First number:15

Second number: 7

Step-by-step explanation:

To find the 2 numbers, we can use system of equations.

Let's use x for the first number and y for the second number. Our first equation would be:

x-y=8

This equation comes from the first sentence: the difference of the 2 numbers is 8. The second equation would be

2x+3y=51

This equation comes from the second part of the question.

We can use elimination method to find x and y.

x-y=8

2x+3y=51

Let's eliminate x. To do so, the x in both equations must be equal to each other. Since one is x and another is 2x, we must multiply the first equation by 2 to get the same x.

2x-2y=16

2x+3y=51

Now that the x are the same, we can subtract the equations.

-5y=-35

y=7

With our y value, we can find x by plugging y into any of the equations.

x-7=8

x=15

Since we found our x and y, the first number is 15 and the second number is 7.