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? Choose the correct choice.
A) 20
B) 40
C) 10
D) 39
E) 48
Let us write the fraction for each group of students   Group A: younger than 10: 50% = 50/100 = 1/2   Group B: 10 years old: 1/20   Group 10: older that 10 but younger than 12: 1/10   Group D: 12 years or older: 70 students   The fraction for group A, B and 10 together is given by   1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator   = 13 / 20 , add numerators   The fraction for group D is given by   20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students   If X is the total number of students, then   7 / 20 of X = 70   or (7 / 20) * X = 70   Solve for X   X = 70 * (20 / 7)= 
<gadget id="calculator">70 * (20 / 7)</gadget>
<output>200</output>
200   Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to   (1 / 20) of 200= 10 students   correct answer 10
<result>C</result>
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?