Question
Of the students taking a gym class, 5 students take cricket for every 4 students who take tennis. This is represented in the diagram. Explain how you can use the diagram to find the number of students who are taking tennis if there are 35 students taking cricket.
Answers
GPT-4o mini
To solve the problem using the ratio and the diagram, let's analyze the given information:
1. The ratio of students taking cricket to those taking tennis is 5:4. This means for every 5 students taking cricket, there are 4 students taking tennis.
2. From the problem, we know there are 35 students taking cricket.
We can express this relationship using the ratio:
Let:
- \( C \) = number of students taking cricket
- \( T \) = number of students taking tennis
According to the ratio, we can write:
\[
\frac{C}{T} = \frac{5}{4}
\]
This can be rearranged to express \( T \) in terms of \( C \):
\[
4C = 5T \implies T = \frac{4}{5}C
\]
3. Now substitute the known value of \( C \) (which is 35):
\[
T = \frac{4}{5} \times 35
\]
4. Calculating that gives:
\[
T = \frac{4 \times 35}{5} = \frac{140}{5} = 28
\]
Thus, the number of students taking tennis is 28.
In the diagram, if you apply the ratio of cricket to tennis (5:4), you could visualize this by dividing the total number of participants into segments that would represent the respective counts of each sport based on their ratio. Since you have already identified the number of students taking cricket (35), you can easily calculate the corresponding number of students for tennis using the defined ratio.
1. The ratio of students taking cricket to those taking tennis is 5:4. This means for every 5 students taking cricket, there are 4 students taking tennis.
2. From the problem, we know there are 35 students taking cricket.
We can express this relationship using the ratio:
Let:
- \( C \) = number of students taking cricket
- \( T \) = number of students taking tennis
According to the ratio, we can write:
\[
\frac{C}{T} = \frac{5}{4}
\]
This can be rearranged to express \( T \) in terms of \( C \):
\[
4C = 5T \implies T = \frac{4}{5}C
\]
3. Now substitute the known value of \( C \) (which is 35):
\[
T = \frac{4}{5} \times 35
\]
4. Calculating that gives:
\[
T = \frac{4 \times 35}{5} = \frac{140}{5} = 28
\]
Thus, the number of students taking tennis is 28.
In the diagram, if you apply the ratio of cricket to tennis (5:4), you could visualize this by dividing the total number of participants into segments that would represent the respective counts of each sport based on their ratio. Since you have already identified the number of students taking cricket (35), you can easily calculate the corresponding number of students for tennis using the defined ratio.