Question 1153397
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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 = {{{7/8}}}


new fraction = {{{(7+x)/(8+2x)}}}


new fraction = {{{8/13}}} (given info)


Set {{{(7+x)/(8+2x)}}} equal to {{{8/13}}}. Solve for x.


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{{{(7+x)/(8+2x) = 8/13}}}


{{{13(7+x) = 8(8+2x)}}} Cross multiply


{{{91+13x = 64+16x}}} Distribute


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


{{{27 = 3x}}} Combine like terms


{{{3x = 27}}}


{{{x = 27/3}}} Divide both sides by 3


{{{x = 9}}} This is the answer.


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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 = {{{(7+x)/(8+2x) = 16/26 = (2*8)/(2*13) = 8/13}}}


The answer is confirmed.


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Answer: <font size=4 color=red>9</font>


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