SOLUTION: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How man

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Question 1055591: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
Answer by ikleyn(52781) About Me  (Show Source):
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In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12,
the remaining 70 students are 12 years or older. How many students are 10 years old?
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Let x = the total number of students in the school.

Then 0.5x are those who are younger than 10;       (1)

     0.05 are 19 years old;                        (2)

     0.1x are older than 10 but younger than 12.   (3)


Their sum (1) + (2) + (3) is 0.5x + 0.05x + 0.1x = 0.65x.


The remaining are x - 0.65x = 0.35x,  and the equation is

0.35x = 70.


Then x = 70%2F0.35 = 200.

Thus there are 200 students in the school.

Hence, 10-years old student's population is 0.1*200 = 20.