Sure, let's solve this problem step by step.
First, we understand the two quantities we have:
- The number of people, which is 50.
- The number of books, which is 4,000.
We want to find the ratio of people to books. A ratio essentially compares two quantities, showing how many times one value is contained within the other.
Step 1: Express the ratio of people to books.
We denote the number of people as [tex]\( P \)[/tex] and the number of books as [tex]\( B \)[/tex]. Thus, we have:
[tex]\[ \text{Ratio of people to books} = \frac{P}{B} = \frac{50}{4000} \][/tex]
Step 2: Simplify the ratio.
To simplify [tex]\( \frac{50}{4000} \)[/tex], we can divide both the numerator and the denominator by their greatest common divisor (GCD). Here, dividing both by 50 gives us:
[tex]\[ \frac{50 \div 50}{4000 \div 50} = \frac{1}{80} \][/tex]
Step 3: Write the ratio in a readable form.
The ratio [tex]\( \frac{1}{80} \)[/tex] can be expressed as:
[tex]\[ 1:80 \][/tex]
Therefore, the ratio of people to books is 1:80.
Comparing this to the given options, the best answer is:
O B. 1:80
