Question

A travel agent surveyed a random sample of her clients on their holiday plans. Of the surveyed clients, 𝑦 out of every 𝑥 number of people want to go to Disneyland. If the agent has 45 clients, find the estimated number of clients who do not want to go to Disneyland.

• A. $\frac{45(x-y)}{y}$
• B. $\frac{45(x-y)}{x}$
• C. $\frac{45x-y}{y}$
• 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 Disneyland.
Number of people (out of 𝑥) who do not want to go to Disneyland $=x-y$
Total clients $=45$
Let the estimated number of clients who do not want to go to Disneyland be $w$.
Then, by proportion, we have:

$\frac{x-y}{x}=\frac{w}{\text{Total number of clients}}$

$\frac{x-y}{x}=\frac{w}{45}$

$w=\frac{45(x-y)}{x}$

Thus, the estimated number of clients who do not want to go to Disneyland is $\frac{45(x-y)}{x}$