SOLUTION: 1 If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number. 2. The sum of a number an its reciprocal is 13/

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: 1 If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number. 2. The sum of a number an its reciprocal is 13/      Log On

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Question 127562This question is from textbook
: 1 If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number.
2. The sum of a number an its reciprocal is 13/6. Find the numbers.
3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool? This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number.
:
Let the number to be added = x
:
%28%28x%2B3%29%29%2F%28%282x%2B7%29%29 = 4%2F7
Cross multiply, and solve for x
4(2x+7) = 7(x+3)
8x + 28 = 7x + 21
8x - 7x = 21 - 28
x = -7
:
Check solution in original equation, substitute -7 for x
%28%28-7%2B3%29%29%2F%28%282%28-7%29%2B7%29%29 =
%28-4%29%2F%28%28-14%2B7%29%29 =
%28-4%29%2F%28-7%29 = 4%2F7; minus into a minus is a plus
:
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2. The sum of a number an its reciprocal is 13/6. Find the numbers.
x + 1%2Fx = 13%2F6
Multiply equation by 6x to get rid of the denominators
6x(x) + 6x*1%2Fx = 6x*13%2F6
6x^2 + 6 = 13x
:
6x^2 - 13x + 6 = 0; a quadratic equation
:
After a little slogging, we find we can factor this to:
(2x - 3)(3x - 2) = 0
:
2x = 3
x = 3%2F2
and
3x = 2
x = 2%2F3
:
Check solution using x = 3/2:
3%2F2 + 2%2F3 = 13%2F6
9%2F6 + 4%2F6 = 13%2F6; confirms our solution
Note that the 2nd solution is the reciprocal of the 1st
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3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool?
:
A typical shared work problem:
Let t = time required when both pipes are open
Let the full pool = 1
:
t%2F5 + t%2F4 = 1
Multiply equation by a common multiple, 20 will work
20*t%2F5 + 20*t%2F4 = 20(1)
Cancel out the denominators and you have:
4t + 5t = 20
:
9t = 20
t = 20%2F9
t = 2.22 hrs or 2 hrs & 13.3 min
:
Check solution using 2.22 for t:
2.22%2F5 + 2.22%2F4 = 1
.444 + .555 = .999 ~ 1; confirms our solution
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Could you follow the procedures in all these problems? Let me know if you have any questions