SOLUTION: I have been trying for two hours to get this, but I can't. Can someone PLEASE help??? One number is 16 more than another. If the smaller number is subtracted from two thirds of

Question 120636This question is from textbook Algebra Structure and Method
: I have been trying for two hours to get this, but I can't. Can someone PLEASE help???
One number is 16 more than another. If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sum of the two numbers. Find the numbers.
This question is from textbook Algebra Structure and Method

Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
:
"One number is 16 more than another."
Smaller number = x
one number = (x+16)
:
"If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sum of the two numbers."
(x+16) - x = ((x+16) + x)
:
(x+16) - x = (2x+16)
:
Multiply equation by 12:
12*(x+16) - 12*x = 12*(2x+16)
Cancel out the denominators and you have:
:
4(2)(x+16) - 12x = 3(2x+16)
8(x+16) - 12x = 6x + 48
8x + 128 - 12x = 6x + 48
:
8x - 12x - 6x = 48 - 128
-10x = -80
x =
x = + 8
and
8 + 16 = 24 is the larger number
:
:
Check solution in the statement:
"If the smaller number is subtracted from two thirds of the larger number, the result is one fourth of the sum of the two numbers."
*24 - 8 = (24+8)
16 - 8 = *32
8 = 8 confirms our solutions
:
Did I make this clear to you? Let me know please, any questions?

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x=smaller, so x+16=larger

((2/3)(x+16))-x=(x+x+16)/4 __ multiply by 12 to clear the fractions

8(x+16)-12x=3(2x+16) __ 8x+128-12x=6x+48 __ 80=10x
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