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A class had 35 students. no grade was lower than a c. there were twice as many c's as b's and 5 more b's than a's. find the number of each grade

User Hilmi
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1 Answer

5 votes

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

User Scrthq
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