Chapter 3.8, Problem 19P

A local parks department asked 300 people if they should build new basketball courts and/or new skateboard ramps. They were not allowed to answer 'neither' If 233 people said they want new basketball courts and 94 people said they want both new basketball courts and skateboard ramps, how many people said they wanted new skateboard ramps?

To determine

To find: The number of people who said that they wanted new skateboard ramps .

Answer to Problem 19P

Number of people who said that they wanted new skateboard ramps is 161

Explanation of Solution

Given information: A local parks department asked 300 people if they should build new basketball courts and /or new skateboard ramps. They are not allowed to answer “neither’.233 people said they wanted new basketball courts and 94 people said they want both new basketball courts and skateboard ramps.

Calculation:

Let the set of people who wanted new basketball courts be represented by set A and the set of people who wanted new skateboard ramps be represented by set B.

Then, according to given information, we have

$n\left(A\cup B\right)=300,n\left(A\right)=233,n\left(A\cap B\right)=94$

Now, we know that

$n\left(A\cup B\right)=n\left(A\right)+n\left(B\right)-n\left(A\cap B\right)$

By substituting the values, we get

$\begin{array}{l}300=233+n\left(B\right)-94\\ 300=139+n\left(B\right)\\ n\left(B\right)=300-139=161\end{array}$

Thus, the number of people who said that they wanted new skateboard ramps is 161