Question

the denominator of a fraction is 1 less than four times the numerator. if 1 is added to both the numerator and the denominator the fraction becomes 3/8. find the number

answer is 2/7​

Answer 1

Answer:

x = 2, y = 7

Step-by-step explanation:

let the fraction be x/y

y = 4x - 1

$\frac{x + 1}{y + 1} = \frac{3}{8} \\ 8(x + 1) = 3(y + 1) \\ 8x + 8 = 3y + 3 \\ 8x - 3y = 3 - 8 \\ 8x - 3y = - 5 \\ 8x - 3(4x - 1) = - 5 \\ 8x - 12x + 3 = - 5 \\ - 4x = - 5 - 3 \\ - 4x = - 8 \\ x = \frac{ - 8}{ - 2} \\ x = 2 \\ y = 4x - 1 \\ y = 4(2) - 1 \\ y = 8 - 1 = \\ therefore \: the \: required \: fraction \: is \: \frac{x}{y} = \frac{2}{7}$