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/

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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)   (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
:
=
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
=
=
= ; minus into a minus is a plus
:
:
2. The sum of a number an its reciprocal is 13/6. Find the numbers.
x + =
Multiply equation by 6x to get rid of the denominators
6x(x) + 6x* = 6x*
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 =
and
3x = 2
x =
:
Check solution using x = 3/2:
+ =
+ = ; confirms our solution
Note that the 2nd solution is the reciprocal of the 1st
:
:
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
:
+ = 1
Multiply equation by a common multiple, 20 will work
20* + 20* = 20(1)
Cancel out the denominators and you have:
4t + 5t = 20
:
9t = 20
t =
t = 2.22 hrs or 2 hrs & 13.3 min
:
Check solution using 2.22 for t:
+ = 1
.444 + .555 = .999 ~ 1; confirms our solution
:
:
Could you follow the procedures in all these problems? Let me know if you have any questions

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