SOLUTION: If a number is added to the numerator of 7 8 and twice as much is added to the denominator, the result is 8 13 . Find the number.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If a number is added to the numerator of 7 8 and twice as much is added to the denominator, the result is 8 13 . Find the number.      Log On


   

Question 1153397: If a number is added to the numerator of
7
8
and twice as much is added to the denominator, the result is
8
13
.
Find the number.
Found 2 solutions by jim_thompson5910, mananth:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x = number added to old numerator

old numerator = 7

new numerator = 7+x

old denominator = 8

new denominator = 8+2x, since twice as much is added here

old fraction = 7%2F8

new fraction = %287%2Bx%29%2F%288%2B2x%29

new fraction = 8%2F13 (given info)

Set %287%2Bx%29%2F%288%2B2x%29 equal to 8%2F13. Solve for x.

-------------------------

%287%2Bx%29%2F%288%2B2x%29+=+8%2F13

13%287%2Bx%29+=+8%288%2B2x%29 Cross multiply

91%2B13x+=+64%2B16x Distribute

91-64+=+16x-13x Separate out common or like terms.

27+=+3x Combine like terms

3x+=+27

x+=+27%2F3 Divide both sides by 3

x+=+9 This is the answer.

-------------------------

Using that x value, we can see that,

new numerator = 7+x = 7+9 = 16
new denominator = 8+2x = 8+2*9 = 26

new fraction = %287%2Bx%29%2F%288%2B2x%29+=+16%2F26+=+%282%2A8%29%2F%282%2A13%29+=+8%2F13

The answer is confirmed.

-------------------------

Answer: 9


Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the number added to the numerator

%287%2Bx%29%2F%288%2B2x%29=8%2F13
13(7+x)=8(8+2x)
91+13x=64+16x
3x=27
x=9