Question

I need help with 3 math questions. Here they are: A study of 50 high school students showed that exactly 25 of them took Biology, exactly 20 of them took Chemistry, and exactly 12 of them took both subjects. How many of the 50 students took neither Biology nor Chemistry? From a pile of coins containing nickels (N), dimes (D), and quarters (Q), Tom picked 10 coins with a total value of $1.00. The 10 coins had a different number of each of the three types and at least 1 coin of each type. How many coins of each type did he pick? An Olympiad team is made up of students from the 4th, 5th, and 6th grades only. Seven students are 5th graders, eleven students are 6th graders, and one third of the entire team are 4th graders. How many students are on the team? If you can even answer one question that would be very helpful! Thanks a lot!

Answer 1

1. Since 12 took both, subtract 12 from 20 and 25. 
Now we have 8 taking only chemistry, 13 taking only biology, and 12 taking both. Add all those together to get 33. 
Subtract 33 from 50 to get 17, which is the number of students taking neither. 

2. He had 3 nickels, 1 quarter, and 6 dimes. 
This is an equation that represented his coins: 
3n + 1q + 6d = 1.00 
3 x .5 = .15    1 x .25 = .25    6 x .10 = .60    .60 + .25 = .85    .85 + .15 = 1.00 

3. Add together 7 and 11 to get the 5th and 6th graders: 18 students. 
The remaining 4th graders make up 1/3 of the team, so 18 is 2/3 of the team.
Find 1/3 by dividing 18 by 2 to get 9. 
There are 9 4th graders. 

Hope this helps!