Question

A survey was conducted in a community to determine whether to build a library or a park. Out of 120 people participated in the survey, the number of people who wanted library is one third of the number of people who wanted park. Also, 22 people wanted both and 22 did not want both.

Compute people who wanted park only
If everyone who wants to build a library contributes 15/15 books, how many books will be collected?

Answer 1

Step-by-step explanation:

Let's denote:

- \( L \) as the number of people who wanted the library only,

- \( P \) as the number of people who wanted the park only,

- \( B \) as the number of people who wanted both,

- \( N \) as the number of people who did not want either the library or the park.

From the given information, we can write the following equations:

1. Total number of people surveyed: \( L + P + B + N = 120 \)

2. Number of people who wanted the library is one-third of the number of people who wanted the park: \( L = \frac{1}{3}P \)

3. Number of people who wanted both: \( B = 22 \)

4. Number of people who did not want either: \( N = 22 \)

To find the number of people who wanted the park only, we can use the equation:

\[ P = \frac{120 - (22 + 22)}{4} = \frac{76}{4} = 19 \]

Now, to find the total number of books collected if everyone contributes 15 books each for the library:

\[ \text{Total number of books} = L \times 15 = \frac{1}{3}P \times 15 \]

Substituting \( P = 19 \) from the previous calculation:

\[ \text{Total number of books} = \frac{1}{3} \times 19 \times 15 = 95 \]

So, a total of 95 books will be collected if everyone who wants to build a library contributes 15 books each.