Mathematical 40213

Sixty-two 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?

Correct answer:

a =  17
b =  24
c =  16
d =  5

Step-by-step 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

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you have a system of equations and looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: