Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to 23. What is the original fraction equal to?

Answer 1

Sorry! I got the answer!

Answer 2

Step-by-step explanation:

Let the numerator be x and denominator be y.

According to the first condition:

x = y - 6..... (1)

According to the second condition:

$\frac{x + 3}{y} = 23 \\ x + 3 = 23y....(2) \\ from \: (1) \: and \: (2) \\ y - 6 + 3 = 23y \\ y - 3 = 23y \\ - 3 = 23y - y \\ - 3 = 22y \\ y = - \frac{3}{22} \\ x = y - 6 = - \frac{3}{22} - 6 \\ = \frac{ - 3 - 132}{22} \\ x = - \frac{135}{22} \\ \frac{x}{y} = \frac{ - \frac{135}{22} }{ - \frac{3}{22} } \\ = - \frac{135}{22} \times - \frac{22}{3} \\ = \frac{135}{3} \\ = \frac{45}{1} = 45 \\ thus \: the \: original \: fraction \: is \: \frac{45}{1} \\ = 45$