To determine the total number of athletes who competed in the track and field meet, we need to use the information given. Here’s the step-by-step solution:
1. Identify the given data:
- The number of athletes who threw the shot put: 24.
- This number represents [tex]\(\frac{15}{100}\)[/tex] (or 15%) of the total athletes at the meet.
2. Understand the problem:
- We know that 24 athletes make up 15% of the total number of athletes. Our goal is to find the total number of athletes.
3. Set up the equation:
Let [tex]\( \text{Total Athletes} \)[/tex] be [tex]\( T \)[/tex].
According to the problem, 24 athletes is 15% of [tex]\( T \)[/tex]:
[tex]\[
24 = \frac{15}{100} \times T
\][/tex]
4. Convert the percentage to a decimal:
- [tex]\(\frac{15}{100} = 0.15\)[/tex]
So the equation becomes:
[tex]\[
24 = 0.15 \times T
\][/tex]
5. Solve for [tex]\( T \)[/tex]:
- To isolate [tex]\( T \)[/tex], divide both sides of the equation by 0.15:
[tex]\[
T = \frac{24}{0.15}
\][/tex]
6. Perform the division:
- Calculating [tex]\(\frac{24}{0.15}\)[/tex]:
[tex]\[
T = 160
\][/tex]
Therefore, the total number of athletes who competed in the meet is [tex]\( 160 \)[/tex].
