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

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=(7x)/(10) \\ Children=(3x)/(10) \end{gathered}`

When 90 adult joins, the number of adult becomes:

`(7x)/(10)+90`

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

It follows:

`(7x)/(10)+90=3((3x)/(10))`

Solving for x gives:

`\begin{gathered} (7x)/(10)-3((3x)/(10))=-90 \\ (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} (3)/(4)y=450 \\ 3y=4(450) \\ y=(4(450))/(3) \\ y=600 \end{gathered}`

Therefore the total number of seats is 600