Chapter 9, Problem 14CT

To determine

To Solve: The system of equations of two variables.

Answer to Problem 14CT

  $\frac{3}{7}$

Explanation of Solution

Given: The numerator of a fraction is $4$ less than the denominator. If $17$ is added to each the value of the fraction $\frac{5}{6}$ . Find the original fraction.

The numerator of a fraction is $4$ less than the denominator

i.e.

  $n=d-4$

Then the fraction becomes

  $\frac{d-4}{d}\mathrm{....}(i)$

If $17$ is added to each the value of the fraction $\frac{5}{6}$

i.e.

  $\frac{d-4+17}{d+17}=\frac{5}{6}$

Solving

  $\begin{array}{l}\frac{d-4+17}{d+17}=\frac{5}{6}\\ 6(d+13)=5(d+17)\\ 6d+78=5d+85\\ 6d-5d=85-78\\ d=7\end{array}$

Substitute $d=7$ in $(i)$

  $\frac{d-4}{d}=\frac{7-4}{7}=\frac{3}{7}$

Hence the original fraction is $\frac{3}{7}$