Chapter 4.1, Problem 76SR

To determine

To Calculate:

If y = 10 when x = 5, find y when x = 6.

Answer to Problem 76SR

y = 12 , when x = 6

Explanation of Solution

Given Information:

If y = 10 when x = 5.

Concept Used:

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol , $\alpha$ .

For example, x and y are two quantities or variables which are linked with each other directly, then we can say $x\alpha y$ . When we remove the proportionality symbol, the ratio of x and y becomes equal to a constant, such as $\frac{x}{y}=C$ , where C is a constant. 

Calculation:

Since y varies directly as x .

  $\begin{array}{l}y=kx\\ 10=k(5)\mathrm{.....................}["y=10"when"x=5"]\\ \frac{10}{5}=\frac{k(5)}{5}\mathrm{...................}[divide"5"each\_side]\\ 2=k\mathrm{...........................}[simplify]\\ \end{array}$

So, the direct variation equation is $y=2x$ .

Substitute x =6 and find y :

  $\begin{array}{l}y=2x\\ y=2(6)\mathrm{.....................}[x=6]\\ y=12\end{array}$

So, y = 12 when x = 6.