How many students in the School IF...

[DanOh62]

How many students go to this school if:

17% play Vollleyball
12% play Soccer

8 students play volleyball and soccer

75% don't play Volleyball or Soccer

Any pointers, tips, url's or answers would be greatly appreciated by this father of a 7th grade student.

Thanks.

 

[HallsofIvy]

How many students go to this school if:

17% play Vollleyball
12% play Soccer

8 students play volleyball and soccer

75% don't play Volleyball or Soccer

Any pointers, tips, url's or answers would be greatly appreciated by this father of a 7th grade student.

Thanks.

Call the total number of student "N". "17% play Volleyball" so .17N students play volley ball. "12% play Soccer" so .12N students play soccer. "8 students play volleyball and soccer" so those 8 students are counted in both- we only want to count them once so we subtract off 8: .17N+ .12N- 8 play soccer or volleyball or both. "75% don't play volleyball or soccer" so .75N students do not do either: adding the people who play "soccer or volleyball or both or neither" gives all the students in school: .17N+ .12N- 8+ .75N= N. Solve that equation for N.

 

[pka]

How many students go to this school if:
17% play Vollleyball
12% play Soccer

8 students play volleyball and soccer
75% don't play Volleyball or Soccer

Here is a second way to do this.
Because 75% do not play either, then 25% participate.
But 17%+12%=29%. That means 4% play both.
Thus 8 is 4% of the total.

 

[DanOh62]

How many students go to this school if: Thank you

Thank you HallsofIvy & pka,

Providing the answer for future references:

.17N + .12N -8 + .75N = 1N <-- Get N's on same side of equation
.17N + .12N -8 +.75N -1N +8 = 1N-1N + 8
.04N=8
.04N/.04=8/.04
1N=200 OR N=200 students

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Here is a second way to do this.
Because 75% do not play either, then 25% participate. -->We know this because the total population is represented by 100%
But 17%+12%=29%. That means 4% play both. --> 29%-25%=4% play both volleyball and soccer
Thus 8 is 4% of the total. --> This sounds odd but how many 4% are in 8 OR 8/.04=200 Students

==========================================================

 

[HallsofIvy]

Thank you HallsofIvy & pka,

Providing the answer for future references:

.17N + .12N -8 + .75N = 1N <-- Get N's on same side of equation
.17N + .12N -8 +.75N -1N +8 = 1N-1N + 8
.04N=8
.04N/.04=8/.04
1N=200 OR N=200 students

=========================================================
Here is a second way to do this.
Because 75% do not play either, then 25% participate. -->We know this because the total population is represented by 100%
But 17%+12%=29%. That means 4% play both. --> 29%-25%=4% play both volleyball and soccer
Thus 8 is 4% of the total. --> This sounds odd but how many 4% are in 8 OR 8/.04=200 Students

==========================================================

That last question "sounds odd" because it strangely phrased! It should be "4% of what number is 8?"