SOLUTION: Please help me with this problem. One third(1/3) of a stack of paper and a one (1) pound book will balance one fourth(1/4) of the stack of paper and 3 of the books - How much do

Algebra ->  Algebra  -> Human-and-algebraic-language -> SOLUTION: Please help me with this problem. One third(1/3) of a stack of paper and a one (1) pound book will balance one fourth(1/4) of the stack of paper and 3 of the books - How much do      Log On

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Question 67177: Please help me with this problem.
One third(1/3) of a stack of paper and a one (1) pound book will balance one fourth(1/4) of the stack of paper and 3 of the books - How much does half the stack of paper weigh?
Thanks for your help.
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the weight of the WHOLE stack of paper (in pounds)
Now, we know 1 book equals 1 pound and 1 book AND 1/3 of the stack (x) = 3 books and 1/4 of the stack (x). This is just a matter of solving for x!
1 + 1%2F3x = 3 + 1%2F4x --- subtract 1 from both sides
1 + 1%2F3x - 1 = 3 + 1%2F4x - 1
1%2F3x = 2 + 1%2F4x ---- subtract 1%2F4x from both sides
1%2F3x - 1%2F4x = 2 --- find the common denominator
4%2F12x - 3%2F12x = 2
%284-3%29%2F12x = 2
1%2F12x = 2 ---- multiply both sides by 12
12 * 1%2F12x = 2 * 12 and ultimately
x = 24.
You can check this answer by plugging back into the original equation.
1 + 1%2F3 * 24 = 3 + 1%2F4 * 24
1 +_8 = 3 + 6
9 = 9
So 1 stack of paper weighs 24 pounds!
Hope this helps!!