Question

Antoine has a carnival booth at the school fair where students randomly select a ping pong ball from a can. He wants to place 5 red ping pong balls an n blue ping pong balls in the can. He also wants the probability of randomly choosing a blue ping pong ball to be 3/5.
Part A:
Write an equation that can be used to model this situation.

Part B:
Solve the equation and interpret the solution in terms of the context, determining if the solution is viable.

Answer 1

Answer:

(a)$5n=3n+15$

(b)$n=7.5$

Solution is not viable

Step-by-step explanation:

(a)

Total number of red ping pong balls$=5$

Total number of red ping pong balls$=n$

Now, probability of an event $=\frac{Number of favourable events}{Total number of events}$

Then, theprobability of randomly choosing a blue ping pong ball is

$=\frac{n}{n+5}$

Given that this probability is$=\frac{3}{5}$

Thus, we have that,

$\frac{n}{n+5}= \frac{3}{5}\\ 5n=3(n+5)\\5n=3n+15$

(b)

Solving, the above equation,

$5n=3n+15\\2n=15\\n=7.5$

This solution is not viable as, number of ping pong ball must be an integer and not a decimal number.