SOLUTION: This is a word problem my son just had on a quiz and I couldn't solve either. I thought we didn't have enough info. Marshfield Middle school cluster C has 100 students in honors

Question 220726: This is a word problem my son just had on a quiz and I couldn't solve either. I thought we didn't have enough info.
Marshfield Middle school cluster C has 100 students in honors pre-algebra
Cluster C has 30 students enrolled in after school math enrichment.
If 105 cluster C students are in only one or the other of these, how many students are in both?
Tried a venn diagram to get my mind around it, didn't work. (I keep thinking I need to know the total enrollment of honors pre-alg plus after school)my son said he got 12.5 as an answer, but the teacher said it would come out as a whole number.
Thanks, Trish
Found 2 solutions by jim_thompson5910, kensson:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = Number of students in both classes

To find the number of students in only one or the other (not both) class, we subtract out the number that are in both (which is 'x') from the total.

In other words,

Number that are in one or other (not both) = (Number in pre-algebra + Number in math enrichment) - (Number in both)

105 = (100+30) - x

105 = 130 - x

105-130 = - x

- 25 = - x

25 = x

x = 25

So there are 25 students in both classes.

Answer by kensson(21) (Show Source): You can put this solution on YOUR website!
I agree with your son, even if the answer doesn't make sense. I reckon the question is badly set up.
Let's call the number of students in (only) honors pre-alg H, the number of students in (only) math enrichment M and the number in both B. We've got:
1) H + B = 100
2) B + M = 30
3) H + M = 105
1 + 2) 2B + H + M = 130
1 + 2 - 3) 2B = 25
B = 12.5
Edit: I disagree with Jim's answer - his working would be correct if there were 105 students in Cluster C altogether.
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