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

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

(b)
`n=7.5`

Solution is not viable

Explanation:

(a)

Total number of red ping pong balls
`=5`

Total number of red ping pong balls
`=n`

Now, probability of an event
`=(Number of favourable events)/(Total number of events)`

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

`=(n)/(n+5)`

Given that this probability is
`=(3)/(5)`

Thus, we have that,

`(n)/(n+5)= (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.