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word problem with percents and fractions

in a school 50% of the students are younger than10 1/20th are 10 years old and 1/10th are older than 10 but younger than12 the remaining 70 students are 12 years or older how many students are 10 years old?
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1 Answer

1/20=.05=5%
1/10=.10=10%
 
This is the breakdown:
Percentage         Age                   Number of Students
50%                 <10                              _b_
5%                     10                              _c_
10%          10<students<12                  _d_
_a__                   12                               70
 
So, our percentages must equal 100% combined and we are missing the percentage for the 12yo:
50%+10%+5%=65%
100%-65%=35%
So a=35%
 
This means 70 children is 35% (or .35) of all of the children.
This is how it looks mathematically:
.35x=70
Where x is the total number of children.
Solve for x. Multiply both sides by the inverse of .35
(1/.35).35x=70*(1/.35)
x=70/.35
x=200
 
The question asks, how many students are 10yo? We know 10yos are 5% (or .05) of the students, and we have 200 students, so:
200*.05=10
So, that value c above is 10.
 
There are 10 students who are 10 years old.