let 'x' be the numerator
'y' be the denominator
[tex] \frac{4}{5} = \frac{x}{y} [/tex]
cross multiplying you'll have
4y = 5x
y = 5/4 x ------equation 1
since the numerator and denominator combined is 15 then the equation will be
x + y =15 ----equation 2
substitute equation 1 to equation 2
x + y = 15
x + 5/4 x = 15
4x + 5x = 15(4)
9x = 60
x = 20/3 ---numerator
substitute x=20/3 to equation 1
y = 5/4 x
y = 5/4 (20/3)
y = 100/12
y = 25/3 ---denominator
note that there will be no whole number( x and y) that could satisfy the problem. the numerator would be 20/3 and the denominator would be 25/3.. you won't be reducing that one since if you do, x+y=15 won't be satisfied
