word problem with percents and fractions

Question

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?

Answer 1

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.