SOLUTION: Could you please help me with some word problems my teacher has assigned? We were told these were not directly from a math book. One number exceeds four times a second number

Question 153257: Could you please help me with some word problems my teacher has assigned? We were told these were not directly from a math book.
One number exceeds four times a second number by four. One third of the larger number exceeds one-half of the smaller by 8. Find both numbers.
I was thinking it was: x+4x+4 I just get so confused on these problems. Could you help me please?
THank you in advance.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
One number exceeds four times a second number by four. One third of the larger number exceeds one-half of the smaller by 8. Find both numbers.
:
Let x = "One number"
Let y = "a second number
:
Write an equation for each statement:
"One number exceeds four times a second number by four."
x = (4y+4)
:
" One third of the larger number exceeds one-half of the smaller by 8."
x = y + 8
Get rid of those annoying denominators multiply equation by 6, results:
2x = 3y + 6(8)
:
2x = 3y + 48
:
Replace x with (4y+4)
2(4y+4) = 3y + 48
8y + 8 = 3y + 48
8y - 3y = 48 - 8
5y = 40
y =
y = 8
then
x = 4(8) + 4
x = 32 + 4
x = 36
:
The two numbers are: 36, 8
:
Check solutions in original equation:
(36) = (8) + 8
12 = 4 + 8
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