Question

last year 1/5 of the students in your class played a sport this year 10 students join the class five of the new students play a sport now 1/4 of the students play a sport how many students are in your class now

Answer 1

60

Explanation:

last year 1/5 of the class played sports, so s = (1/5) c

the next year, s increased by 5, c increased by 10 and the fraction changed to 1/4, so for the next year (s+5) = (1/4)(c+10)

To solve this we can substitute s = (1/5)c from the first equation into the second, so

((1/5)c + 5)=(1/4)(c+10), simplify both sides

(1/5)c + 5 = (1/4)c + 10/4, simplify 10/4 to 5/2

(1/5)c + 5 = (1/4)c + 5/2, multiply both sides by 20 to eliminate fractions (least common multiple of 2, 4 and 5)

4c + 100 = 5c + 50, subtract 4c, subtract 50 from both sides

50 = c, number of students in class last year was 50, this year is 10 more, so this year is 60