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A school offers both Spanish and Chinese language classes. This past week,10 students dropped from the Chinese classes, which increased the number of students who take neither class from 27 to 31. 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.

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For the record, it's not -6 or -4

 Apr 22, 2023
 #1
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+1

Let's denote the number of students who take the Chinese class as "C", the number of students who take the Spanish class as "S", and the number of students who take neither class as "N".

Initially, we have: C + S + N = Total number of students We don't know the total number of students, but we do know that N = 27.

After 10 students dropped from the Chinese class, we have: (C - 10) + S + (N + 10) = Total number of students We also know that N + 10 = 31, so N = 21.

Substituting N = 21 into the first equation, we get: C + S + 21 = Total number of students

Subtracting this equation from the second equation, we get: (C - 10) + S + 31 = Total number of students

(C + S + 21 = Total number of students)

-10 + 0 + 10 = 0

Therefore, the change did not impact the number of students who take the Spanish class but not the Chinese class (i.e., the difference between S and (S and C)). The answer is 0.

 Apr 22, 2023
 #2
avatar+80 
+1

After 10 students dropped from the Chinese class, we have: (C - 10) + S + (N + 10) = Total number of students.

That is not true. Just because people dropped from the Chinese class (hence the -10) doesn't mean that they weren't in the Spanish class, so you can't do N+10.

Thank you so much for trying, though. I really appriceate your effort!

BTW, I'm totalkoolnezz, just not signed in.

 Apr 22, 2023
edited by Guest  Apr 22, 2023
 #3
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+1

The number of students who take Spanish but not Chinese class decreased by 4.

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.

 Apr 22, 2023
 #4
avatar+80 
0

That should be the anser, but it's not. Strange. Thank so much anyways! :)

 Apr 23, 2023
 #5
avatar+80 
0

*answer

 Apr 23, 2023
 #6
avatar+118594 
+1

It went up by 6

 

Initially    

S students took only spanish

C stuents took Chinese

B students took both

27 did neither.

Total number of students = S+C+B+27

 

The total number of 10 sudeents dropped chines but the number doing neither only went up by 4

Those 4 had to come from the Chines only group, the other 6 came from the both group.

 

So now there are

C-4   students doing chinese

B-6 students doing both

S+6 srtdents doing only chinese

and 31 doing neither

Total number of students =   C-4  +  B-6  +  S+6    +31 =  C+B+S+ 27

 Apr 23, 2023
 #7
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0

TYSM it was correct!

Guest Apr 23, 2023

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