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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.

Respuesta :

Answer:

(a)[tex]5n=3n+15[/tex]

(b)[tex]n=7.5[/tex]

Solution is not viable

Step-by-step explanation:

(a)

Total number of red ping pong balls[tex]=5[/tex]

Total number of red ping pong balls[tex]=n[/tex]

Now, probability of an event [tex]=\frac{Number of favourable events}{Total number of events}[/tex]

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

[tex]=\frac{n}{n+5}[/tex]

Given that this probability is[tex]=\frac{3}{5}[/tex]

Thus, we have that,

[tex]\frac{n}{n+5}= \frac{3}{5}\\ 5n=3(n+5)\\5n=3n+15[/tex]

(b)

Solving, the above equation,

[tex]5n=3n+15\\2n=15\\n=7.5[/tex]

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