Chapter 6.5, Problem 39HP

To determine

To find: the value of $c$ .

Answer to Problem 39HP

  $c=45$

Explanation of Solution

Given information:

$a:b=2:4$ and $b:c=4:9$ , if $a=10$ .

Calculation:

Consider the ratios $a:b=2:4$ and $b:c=4:9$ .

Consider the ratio

  $a:b=2:4$ .

Substitute $a=10$ and solve the value of $b$ .

  $\begin{array}{c}\frac{a}{b}=\frac{2}{4}\\ \frac{10}{b}=\frac{2}{4}\\ 10\left(4\right)=2\left(b\right)\text{Cross}\text{products}\\ \text{40=2b}\text{Multiply}\\ \text{20=b}\text{Divide}\text{by}\text{2}\end{array}$

Thus, $a=10$ implies that $b=20$ .

Consider the ratio $b:c=4:9$ .

Substitute $b=20$ and solve the value of $c$ .

  $\begin{array}{c}\frac{b}{c}=\frac{4}{9}\\ \frac{20}{c}=\frac{4}{9}\\ 20\left(9\right)=c\left(4\right)\\ 180=4c\\ 45=c\end{array}$

Hence, the required value id $c=45$ .