Question

3/4 of the seats in a concert hall were occupied. The ratio of adults to children is 7 : 3. If 90 more adults attended the concert. the number of adults would be 3 times the number of children. How many seats were in the concert hall?

Answer 1

SOLUTION

The given ratio of adults to childeren is:

$7:3$

Let the total number of people be x then the number of adult and chlderen is:

$\begin{gathered} Adult=\frac{7x}{10} \\ Children=\frac{3x}{10} \end{gathered}$

When 90 adult joins, the number of adult becomes:

$\frac{7x}{10}+90$

It is given that the number of adults would be 3 times the number of children.

It follows:

$\frac{7x}{10}+90=3(\frac{3x}{10})$

Solving for x gives:

$\begin{gathered} \frac{7x}{10}-3(\frac{3x}{10})=-90 \\ \frac{7x-9x}{10}=-90 \\ -2x=-900 \\ x=450 \end{gathered}$

Therefore the total number of people is 450.

It is given that 3/4 of the seat were occupied.

Let the total number of seats be y, it follows:

$\begin{gathered} \frac{3}{4}y=450 \\ 3y=4(450) \\ y=\frac{4(450)}{3} \\ y=600 \end{gathered}$

Therefore the total number of seats is 600