SOLUTION: I hope you can help me.. I am learning algebra, however my teacher gave us this problem to due today.. My mother and father came up with 2 different answers.. I am confused.. Here

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I hope you can help me.. I am learning algebra, however my teacher gave us this problem to due today.. My mother and father came up with 2 different answers.. I am confused.. Here       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 78855: I hope you can help me.. I am learning algebra, however my teacher gave us this problem to due today.. My mother and father came up with 2 different answers.. I am confused.. Here is the problem..
Ten students in a class play soccer and 12 students play basketball. Seven students play both soccer and basketball. Half of the students in the class don't play either sport. How many students are in the class? (i did make a venn diagram ).. any help on this would be great.. thanks..VB
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw out a Venn Diagram you will have 10 students in one circle, 12 in another and 7 in the intersection. Since 7 kids play both this means there are 3 kids that only play soccer (since 10-7=3) and 5 kids only play basketball (since 12-7=5). So our total so far is
3+5+7=15
This means 15 kids play a sport. So if we have x as the number of kids in the class we have this many kids who don't play sports
number of kids who don't play sports
y=x-15
Since half of the kids don't play sports we can say
y=%281%2F2%29x
Now substitute x-15 in for y
x-15=%281%2F2%29x
Subtract x from both sides
-15=%281%2F2%29x-x

-15=-%281%2F2%29x
Multiply both sides by -2
%28-2%29%28-15%29=x
So we have x=30 this means there are 30 kids in the class