SOLUTION: The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. Find the numbers.

Question 137580This question is from textbook
: The sum of two numbers is twice their difference. The larger number is 6 more than twice the smaller. Find the numbers. This question is from textbook

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=the larger number
and y=the smaller number
Now we are told that:
x+y=2(x-y) or
x+y=2x-2y subtract x and also y from each side
0=2x-x-2y-y collect like terms
x-3y=0---------------------------------------------eq1
We are also told that:
x=2y+6 subtract 2y from each side
x-2y=2y-2y+6
x-2y=6---------------------------------------------eq2
From eq1, we see that x=3y. Substitute this into eq2
3y-2y=6
y=6---------------------------------------smaller number
substitute y=6 into eq1
x-18=0 add 18 to each side
x=18-------------------------------------larger number
CK
The sum of two numbers is twice their difference:
6+18=2*(18-6)
24=2*12
24=24
The larger number is 6 more than twice the smaller.
18=2*6+6
18=12+6
18=18

Hope this helps---ptaylor
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