Chapter SH, Problem 6.5.1EP

To determine

To calculate: The solution of the proportion.

Answer to Problem 6.5.1EP

The required solution is 9.

Explanation of Solution

Given information:

The proportion: $\frac{7}{k}=\frac{49}{63}$

Calculation:

The given proportion is $\frac{7}{k}=\frac{49}{63}$ .

To find the solution of the given expression, find the greatest common factor of 49 and 63 in the above proportion.

  $49=7\times 7$

  $63=7\times 3\times 3$

So, the greatest common factor of 49 and 63 is 7.

Divide the right hand side of the above proportion by 7.

  $\begin{array}{c}\frac{7}{k}=\frac{\frac{49}{7}}{\frac{63}{7}}\\ \frac{7}{k}=\frac{7}{9}\end{array}$

Apply cross-multiplication on the above proportion and simplify for k .

  $\begin{array}{c}\frac{7}{k}=\frac{7}{9}\\ 7\times k=7\times 9\\ 7k=63\end{array}$

Divide both sides of the above expression by 7.

  $\begin{array}{c}\frac{\cancel{7}k}{\cancel{7}}=\frac{{\cancel{63}}^9}{\cancel{7}}\\ k=9\end{array}$

Hence, the required solution is 9.