Question

The ratio in the number of students in three classes is 3 : 4 : 5. If 20 students are increased in every class, then this ratio becomes 4 : 5 : 6. What was the original number of students in these classes taken together ?

A. 280
B. 240
C. 320
D. 300

Answer 1

To solve this problem, set up equations using the given ratios and use substitution to find the value of x. Then, calculate the original number of students by multiplying the value of x by the ratios. The original number of students in these classes taken together is 240.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's denote the original number of students in the three classes as follows:

• Class A: 3x
• Class B: 4x
• Class C: 5x

After increasing the number of students in each class by 20, the new ratios become:

• Class A: (3x + 20)
• Class B: (4x + 20)
• Class C: (5x + 20)

We can now set up the following equation:

(3x + 20) : (4x + 20) : (5x + 20) = 4 : 5 : 6

Cross multiplying, we get:

4(5x + 20) = 5(4x + 20) = 6(3x + 20)

Simplifying, we get:

20x + 80 = 20x + 100 = 18x + 120

Since all the terms are equal, we can set any two of the equations equal to each other:

20x + 80 = 18x + 120

Simplifying, we get:

2x = 40

Dividing by 2, we find that x = 20.

Now we can find the original number of students in the three classes taken together:

3x + 4x + 5x = 12x = 12 * 20 = 240

Therefore, the original number of students in these classes taken together is 240.