Chapter 8.1, Problem 6PSA

a

To determine

To find: The ratio ofx and y if $2x=3y$

Answer to Problem 6PSA

  $$ Ratio of x and y is 3: 2

Explanation of Solution

Given information

  $2x=3y$

Formula used

  $\frac{a}{b}=a:b$

Calculation:

  $\begin{array}{l}2x=3y\\ \frac{x}{y}=\frac{3}{2}\end{array}$

\ $\Rightarrow x:y=3:2$

b

To determine

To find: The ratio ofx and y if $6\left(y+3\right)\text{=}2\left(x+9\right)$

Answer to Problem 6PSA

  $$ Ratio of x and yis 1: 3

Explanation of Solution

Given information:

  $6\left(y+3\right)\text{=}2\left(x+9\right)$

Formula used:

  $\frac{a}{b}=a:b$

Calculation

Given,

  $\begin{array}{l}6\left(y+3\right)=2\left(x+9\right)\\ \Rightarrow 6y+18=2x+18\\ \Rightarrow 6y=2x\\ \Rightarrow \frac{x}{y}=\frac{2}{6}=\frac{1}{3}\\ \Rightarrow x:y=1:3\end{array}$

c

To determine

To find: The ratio ofx and y if $\frac{3}{x+5}=\frac{9}{y+15}$

Answer to Problem 6PSA

  $$ Ratio of x and yis 1: 3

Explanation of Solution

Given information:

  $\frac{3}{x+5}=\frac{9}{y+15}$

Formula used:

  $\frac{\text{a}}{\text{b}}=\text{a : b}$

Calculation

Given,

  $\begin{array}{l}\frac{3}{x+5}=\frac{9}{y+15}\\ \Rightarrow 3\left(y+15\right)=9\left(x+5\right)\\ \Rightarrow 3y=9x\\ \Rightarrow \frac{x}{y}=\frac{3}{9}=\frac{1}{3}\\ \Rightarrow x:y=1:3\end{array}$