Answer:
The number of a's was 5, the number of b's was 10, and the number of c's was 20
OR
5 students got a grade, 10 students got b grade, 20 students got c grade
Explanation:
Number of students = 35
No grade was lower than c,
i.e. the grades were a, b, and c
We need to find the number of each grade,
Now,
To make it easier for us,
Let the number of students who got a grade be a,
the number of students who got b grade be b
the number of students who get c grade be c
So,
Their sum must equal the total number of students,
a + b + c = 35,
There were twice as many c's as b's, so,
c = 2b
There were 5 more b's than a's
b = a + 5
We get the system of equations,
a + b + c = 35 (i)
c = 2b (ii)
b = a + 5 (iii)
Solving,
Putting value of c and b from (ii) and (iii) into (i),
a + (a + 5) + (2b) = 35
a + a + 5 + 2(a+5) = 35
2a + 5 + 2a + 10 = 35
4a + 15 = 35
4a = 35 - 15
4a = 20
a = 5
There were 5 a's
Putting value of a into (iii) to find b,
b = a + 5,
b = 5 + 5,
b = 10
There were 10 b's
Putting value of b into (ii) to find c,
c = 2b
c = 2(10)
c = 20
There were 20 c's