Question

The ratio of violinists to cellists in the school orchestra must always be 7:3. If the school orchestra has 21 violinists, what is the combined number of cellists and violinists?

Answer 1

Given:

Violinists : Cellists = 7:3.

Number of violinists in the school orchestra = 21

To find:

The combined number of cellists and violinists.

Solution:

Let the number of violinists and cellists in the school orchestra are 7x and 3x respectively.

Then, combined number of cellists and violinists is

`\text{Combined number of cellists and violinists}=7x+3x`

`\text{Combined number of cellists and violinists}=10x` ...(i)

Number of violinists in the school orchestra = 21

`7x=21`

Divide both sides by 7.

`x=3`

Now, the combined number of cellists and violinists is

`\text{Combined number of cellists and violinists}=10(3)` [Using (i)]

`\text{Combined number of cellists and violinists}=30`

Therefore, the combined number of cellists and violinists is 30.