Question

A travel agent surveyed a random sample of her clients about their holiday plans. Of the surveyed clients, $y$ out of every $x$ number of people want to go to the water park. If the agent has $45$ clients, find the estimated number of clients who do want to go to the water park.

• A. $\frac{45x-y}{y}$
• B. $\frac{45(x-y)}{x}$
• C. $\frac{45(x-y)}{y}$
• D. $\frac{45(y-x)}{y}$

Answer 1

The correct option is B $\frac{45(x-y)}{x}$

$y$ out of every $x$ number of people want to go to the water park.
Number of people (out of $x$) who do not want to go to the water park $=x-y$
Total clients $=45$
Let the estimated number of clients who do not want to go to the water park be $w.$
Using proportionality, we get:
$\frac{x-y}{x}=\frac{\text{w}}{\text{total number of clients}}$
$\frac{x-y}{x}=\frac{w}{w}=45(x-y)45$
$w=\frac{45(x-y)}{x}$
Hence, the estimated number of clients who do not want to go to the water park is $\frac{45(x-y)}{x}$.