Question

62 high school students took part in the mathematical olympiad. there were 7 fewer first year students than sophomores, two thirds of the number of third year students, and 5 fourth year students. how many students from each grade took part in the competition?

Answer 1

Answer:a = 17

b = 24

c = 16

d = 5

Explanation:

a+b+c+d=62

a = b-7

c = 2/3·b

d = 5

a+b+c+d = 62

a-b = -7

2b-3c = 0

d = 5

Row 2 - Row 1 → Row 2

a+b+c+d = 62

-2b-c-d = -69

2b-3c = 0

d = 5

Row 3 + Row 2 → Row 3

a+b+c+d = 62

-2b-c-d = -69

-4c-d = -69

d = 5

d = 5/1= 5

c = -69+d/-4= -69+5/-4= 16

b = -69+c+d/-2= -69+16+5/-2 = 24

a = 62-b-c-d = 62-24-16-5 = 17

a = 17

b = 24

c = 16

d = 5