Question

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to 2/3 . If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

Answer 1

The two equation which can be used to solve the problem are:

5n - 3d = 0 and 3n - 2d = -2

Solution:

The numerator of the fraction is "n" and the denominator of the fractions is "d"

The numerator and denominator of a fraction are in the ratio of 3 to 5

numerator : denominator = 3 : 5

$\frac{numerator}{denominator} = \frac{3}{5}$

$\frac{n}{d} = \frac{3}{5}$

On cross-multiplication we get,

5n = 3d

5n - 3d = 0

This is our first equation

The numerator and denominator are both increased by 2, the fraction is now equal to 2/3

The new numerator will be n + 2 and denominator will be d + 2

$\frac{n + 2}{d + 2} = \frac{2}{3}$

On cross multiplication we get,

3(n + 2) = 2(d + 2)

3n + 6 = 2d + 4

3n - 2d = -2

This is our second equation

Thus the two equation which can be used to solve the problem are:

5n - 3d = 0 and 3n - 2d = -2