Question

in a group of 75 campers, boys outnumber girls by a 3:2 ratio. how many more girl campers would have to join the group to give it a 1:1 ratio of boys to girls?

a 6
b 9
c 10
d 12
e 15

Explanation:

Define variables and set up equations

Let \(B\) represent the number of boys and \(G\) represent the number of girls in the group.
The total number of campers is 75:

$$B + G = 75$$

Use the given ratio to find the number of boys and girls

The problem states that boys outnumber girls by a \(3:2\) ratio:

$$\frac{B}{G} = \frac{3}{2} \implies B = 1.5G$$

Substitute \(B = 1.5G\) into the total sum equation:

$$1.5G + G = 75$$

$$2.5G = 75$$

$$G = 30$$

Now, find the number of boys:

$$B = 75 - 30 = 45$$

Calculate the required number of additional girls

To achieve a \(1:1\) ratio of boys to girls, the number of girls must equal the number of boys.
Let \(x\) be the number of additional girls needed:

$$G + x = B$$

$$30 + x = 45$$

$$x = 15$$

Answer:

• (A) 6
• (B) 9
• (C) 10
• (D) 12
• (E) 15 (Correct answer)