The numerator of a fraction (which is in its simplest form) is 5 less than the denominator. if the numerator is multiplied by 2, and the denominator is increased by 16, then the fraction becomes smaller by 1/3 of it. find the original fraction.

n = d - 52n/(d + 16) = n/d - 1/3 n/d2n/(d + 16) = 2/3 n/d Divide by 2n1 / (d + 16) = 1/3 dHere's the tricky part.d + 16 = 3d the two denominators are equal. the numerators are both 1.16 = 2dd = 8so the numerator is d - 5n = 8 - 5n = 3Let's see if it checks out.n = 3d = 82*3 = 68 + 16 = 24New fraction 6/24 = 1/4(3/8 - 1/3 ) = 1/83/8 - 1/8 = 1/4 so it checks with the original conditions put on it.

Step-by-step explanation:

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.