Short Answer
Note: Your teacher will grade your response to ensure that you receive proper credit for your answer.
The graph below shows the number of new clients brought into Sunnydays Insurance Company. Why is the graph misleading?
A line graph is shown.
3 answers
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Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of
his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math
and nothing else
How many students take exactly 2 classes with Mr. Green?
Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of
his classes. He teaches band to 25 students. There are 9 students who have Mr. Green for math
and nothing else
How many students take exactly 2 classes with Mr. Green?
Let's denote the number of students who take choir and math with Mr. Green as A and the number of students who take both band and choir (but not math) as B. We know that:
- The total number of students who take at least one class is 57.
- The number of students who take band is 25.
- The number of students who take only math is 9.
- We want to find the number of students who take exactly 2 classes.
Using this information, we can set up the following equation:
25 + A + B + 9 = 57
Simplifying this equation, we get:
A + B = 23
We know that B represents the number of students who take both band and choir but not math. Let's now find B:
B = 25 - the number of students who only take band
We don't know the number of students who only take band, but we do know that:
- If there were no students who only took band, then B would be 0 and A would be 23 (since A + B = 23). However, we know that there are students who only take band (otherwise the total number of students taking at least one class would be less than 25).
- If all 25 students who take band also take at least one other class with Mr. Green, then A would be 0 and B would be 25. However, we know that there are students who only take math (otherwise the total number of students taking at least one class would be at least 34).
Therefore, the only possibility is that some students take only band and some take both band and choir. Let's denote the number of students who only take band as C:
B + C = 25
Substituting B = 25 - C into the equation A + B = 23, we get:
A + 25 - C = 23
Simplifying, we get:
A = C - 2
We want to find the number of students who take exactly 2 classes. This includes the students who take both band and choir (i.e., B) and the students who take choir and math (i.e., A). Therefore:
Number of students who take 2 classes = A + B = (C - 2) + B = C - 2 + (25 - C) = 23
So, there are 23 students who take exactly 2 classes with Mr. Green.
- The total number of students who take at least one class is 57.
- The number of students who take band is 25.
- The number of students who take only math is 9.
- We want to find the number of students who take exactly 2 classes.
Using this information, we can set up the following equation:
25 + A + B + 9 = 57
Simplifying this equation, we get:
A + B = 23
We know that B represents the number of students who take both band and choir but not math. Let's now find B:
B = 25 - the number of students who only take band
We don't know the number of students who only take band, but we do know that:
- If there were no students who only took band, then B would be 0 and A would be 23 (since A + B = 23). However, we know that there are students who only take band (otherwise the total number of students taking at least one class would be less than 25).
- If all 25 students who take band also take at least one other class with Mr. Green, then A would be 0 and B would be 25. However, we know that there are students who only take math (otherwise the total number of students taking at least one class would be at least 34).
Therefore, the only possibility is that some students take only band and some take both band and choir. Let's denote the number of students who only take band as C:
B + C = 25
Substituting B = 25 - C into the equation A + B = 23, we get:
A + 25 - C = 23
Simplifying, we get:
A = C - 2
We want to find the number of students who take exactly 2 classes. This includes the students who take both band and choir (i.e., B) and the students who take choir and math (i.e., A). Therefore:
Number of students who take 2 classes = A + B = (C - 2) + B = C - 2 + (25 - C) = 23
So, there are 23 students who take exactly 2 classes with Mr. Green.
1 answer