Question 597313
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In the fraction *[tex \Large \frac{4}{7}], 4 is the numerator and 7 is the denominator.


Let *[tex \Large x] represent the as yet unknown numerator.  Then the denominator of the unknown fraction must be *[tex \Large x\ +\ 15].  Hence, a representation of the fraction you want is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{x\ +\ 15}]


And finally, you are given that the value of this fraction is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{7}]


Therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x}{x\ +\ 15}\ =\ \frac{4}{7}]


Since we know that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{a}{b}\ =\ \frac{c}{d}]


is equivalent to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ ad\ =\ bc]


We can cross-multiply to get:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7x\ =\ 4(x\ +\ 15)]


Now just solve the equation for *[tex \Large x], then calculate *[tex \Large x\ +\ 15], and construct the desired fraction.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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