MHB Counting Problem: In a school 315 girls play at least one sports

AI Thread Summary
In a school, 315 girls participate in at least one sport, with 100 in fall, 150 in winter, and 200 in spring sports. A Venn diagram is suggested to visualize the relationships among the groups. The formula for calculating the total number of participants across overlapping sets is provided, which includes intersections of the sets. It is noted that while specific intersections are not given, the total for girls playing exactly two sports is known to be 75. The goal is to determine how many girls play all three sports.
Avro1
Messages
1
Reaction score
0
In a school 315 girls play at least one sport. 100 play a fall sport, 150 play a winter sport, and 200 play a spring sport. If 75 girls play exactly 2 sports, how many play three?
 
Mathematics news on Phys.org
Hello, and welcome to MHB! (Wave)

I would begin by constructing a Venn diagram:

View attachment 9104

We've got 7 variables...can you construct equations involving these variables from the given information?
 

Attachments

  • mhb_0010.png
    mhb_0010.png
    9.6 KB · Views: 119
Hi Avro.

You can also use this formula for any sets $A$, $B$, $C$:
$$|A\cup B\cup C|\ =\ |A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|.$$
So, in this problem, $A$ might be the set of girls playing fall sports, $B$ the set of those playing winter sports, and $C$ the set of those playing spring sports; then you want to find $|A\cap B\cap C|$. Also, note that while you are not given $|A\cap B|$, $|B\cap C|$ or $|C\cap A|$ separately, you are given $|A\cap B|+|B\cap C|+|C\cap A|$, which you can use in the formula above
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Back
Top