Question

A rectangular auditorium seats 3300 people. The number of seats in each row exceeds the number of rows by 16. Find the number of seats in eachrow.

Answer 1

Take x as the number of rows and y as the number of seats in each row.

There are 3300 seats in the auditorium, which means that the product of x and y is 3300:

`x\cdot y=3300`

We also know that y exceeds x by 16, this is:

`y=x+16`

Use these equations to find the number of seats and rows.

`\begin{gathered} x\cdot(x+16)=3300 \\ x^2+16x=3300 \\ x^2+16x-3300=0 \end{gathered}`

Use the quadratic equation to find x:

`\begin{gathered} x=\frac{-16\pm\sqrt[]{16^2-4(1\cdot-3300)}}{2\cdot1} \\ x=(-16\pm116)/(2) \\ x1=(-16+116)/(2)=(100)/(2)=50 \\ x2=(-16-116)/(2)=(-132)/(2)=-66 \end{gathered}`

As x is the number of rows, it can take negative values, so take the value of 50.

Use this values to find y:

`\begin{gathered} x\cdot y=3300 \\ y=(3300)/(x) \\ y=(3300)/(50) \\ y=66 \end{gathered}`

There are 50 seats in each row and there are 66 rows.