Question

In a school orchestra, the ratio of girls to boys is 3 : 2. There are 75 students in the orchestra. How many boys are there in the orchestra?​

Answer 1

30 boys

Explanation:

Let the number of girls be 3x and the number of boys be 2x.

We know that the total number of students is 75:

3x + 2x = 75

Combining like terms, we get:

5x = 75

Dividing both sides by 5, we get:

`\sf (5x)/(5)=(75)/(5)`

x = 15

Therefore, the number of boys in the orchestra is 2x. which is equal to 2 × 15 = 30.

So, There are 30 boys in the orchestra.

Answer 2

30 boys

Explanation:

To find the number of boys in the orchestra, we can first find the total number of parts in the ratio and then determine the number of boys.

The given ratio of girls to boys is 3 : 2, which means there are a total of 3 + 2 = 5 parts in the ratio.

Next, we need to find out how many students represent one part of the ratio. To do this, divide the total number of students (75) by the total number of parts (5):

`\frac{\textsf{Total students}}{\textsf{Total parts}} = \sf (75)/(5) = 15\; \textsf{students per part}`

Now that we know that one part represents 15 students, we can find the number of boys by multiplying the number of parts for boys (2) by the number of students per part (15):

`\textsf{Number of boys} = \sf 2 \; parts * 15\; students/part = 30 \;boys`

So, there are 30 boys in the orchestra.