SOLUTION: Having trouble setting this up. Do I need more information? One number is two times another. Eight times the smaller is two more than twice the larger number. What are the two num

Question 2853: Having trouble setting this up. Do I need more information?
One number is two times another. Eight times the smaller is two more than twice the larger number. What are the two numbers?
Answer by xcentaur(357) (Show Source): You can put this solution on YOUR website!
You have all the information you need from the question itself.
Let the numbers be x,y.
"One number is two times another."
Then, x=2y ..................... [Statement 1]

Now y is half of x (from statement 1).
Therefore x>y.
"Eight times the smaller is two more than twice the larger number."
Then, 8y = 2x + 2 .....................[Statement 2]
Substituting (x=2y) in the second equation we get,
8y = 2(2y) + 2
8y = 4y + 2
8y - 4y = 2
4y = 2
y = (2/4)
Therefore, y=1/2
x=2y => x=2(1/2) => x=1
Therefore we get,
x=1
y=(1/2)
Solution crosscheck:
Puttting these solved values of x and y in the 2nd equation we get,
8(1/2) = 2(1) + 2
4 = 2 + 2
4 = 4
As Lefthand side (LHS) and Righthand side (RHS) are equal,
solved values of x and y are correct.
Hope this helps,
Best of luck.

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