SOLUTION: The sum of two numbers is twice their difference. The larger number is 8 more than twice the smaller. Find the numbers.

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Question 357569: The sum of two numbers is twice their difference. The larger number is 8 more than twice the smaller. Find the numbers.
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!
Let the large number be x.

Let the smaller number be y.

Therefore, we are given

x%2By=2%28x-y%29 and x=2y%2B8

x%2By=2x-2y and x=2y%2B8

x=3y and x=2y%2B8

Then we must solve this system of equations. So by substitution

3y=2y%2B8

y=8

If y=8 then

x=%282%2A8%29%2B8

x=24

The larger number is 24, the smaller number is 8.

I hope this helps!