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A school offers both Spanish and Chinese language classes. This past week,  students dropped from the Chinese classes, which increased the number of students who take neither class from  to . How did this change impact the number of students who take the Spanish class but not the Chinese class?

Enter positive numbers to indicate an increase and negative numbers to indicate a decrease.

 

It's not -6, -4, or 0.

 Apr 23, 2023
 #1
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+1

Let S be the number of students who take Spanish, C be the number of students who take Chinese, and N be the number of students who take neither. We know that S+C+N is constant.

Initially, we have S+C+N0​=N.

After 10 students dropped from Chinese class, we have S+C−10+N1​=N.

We also know that N1​=N0​+4.

Substituting the second equation into the first equation, we get:

S+C−10+N0​+4=N0​

S+C−6=N0​

Subtracting the third equation from the first equation, we get:

S+C+N0​−(S+C−6)=N−(N0​+4)

6=4

Therefore, the number of students who take Spanish but not Chinese class decreased by 4.

However, this is incorrect. The number of students who take Spanish but not Chinese class cannot decrease by 4 because the number of students who take neither class increased by 4. In fact, the number of students who take Spanish but not Chinese class must have increased by 4.

Here is a possible explanation for the discrepancy:

The 10 students who dropped from Chinese class may have been taking Spanish as well.

The 4 students who started taking neither class may have been taking Spanish as well.

Either way, the number of students who take Spanish but not Chinese class must have increased by 4.

 Apr 23, 2023
 #2
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+1

Let S represent the students taking Spanish, C the students taking Chinese, and N the students taking neither language. S+C+N is a constant, as is well known.

At the outset, S+C+N0=N.

After having ten students withdraw from Chinese class, the final enrollment is S+C10+N1.

It is also known that N1 = N0 + 4.

To see what happens when we plug the second equation into the first, we do the following:

S+C−10+N0​+4=N0​

S+C−6=N0​

When we take the difference between the first and third equations, we get:

S+C+N0​−(S+C−6)=N−(N0​+4)

6=4

As a result, there are now 4 fewer students who choose Spanish over Chinese.

But that is not the case. Since there are now 4 more students who take neither Spanish nor Chinese, the number of those who take only Spanish cannot decrease by 4. It's likely that there are now four more students than before who choose Spanish over Chinese.

Possible reasons for the discrepancy are as follows:

Ten of the former Chinese students may have been enrolled in Spanish as well.

It's possible that the four students who initially enrolled in neither class are actually taking Spanish as well.

It's safe to assume that there are now four more students opting for Spanish over Chinese. FLYINGTOGETHER
 

 Apr 23, 2023

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