Chapter 8.10, Problem 9P

To determine

To find:

The equation given that the statement

Answer to Problem 9P

The value is $y_2=22$

Explanation of Solution

Given:

  $x_1,y_1$ varies directly as $x_2,y_2$

Concept used:

If the quantities $x$ and $y$ are related by an equation

  $y=kx$

For some constant $k\ne 0$

That is y varies directly as $x$ or y is directly proportional to $x$

The constant $k$ is called constant proportionality

Calculation:

If the quantities $a_1,b_1$ and $a_2,b_2$ are related by an equation

  $a_1{b}_1\alpha b_2$

  $\begin{array}{l}{a}_1{b}_1=a_2{b}_2\\ x_1{y}_1=x_2{y}_2\\ 25.8\times 440=516\times y_2\\ y_2=\frac{25.8\times 440}{516}\\ y_2=\frac{258\times 44}{516}\\ y_2=22\end{array}$

For some constant $k\ne 0$

That is $a_1,b_1$ varies directly as $a_2,b_2$ or $a_1,b_1$ is directly proportional to $a_2,b_2$

The constant $k$ is called constant proportionality