The seating capacity of an auditorium is 300. The seats are categorised as 1, 2, 3 and 4. The costs of the tickets in the categories are in the table below.

1. Find the number of CAT 4 seats using the given ratio.

Total ratio parts $=1+2+4+5=12$

Number of CAT 4 seats $=\dfrac{5}{12}\times 300=125$

2. Calculate the ticket sales for CAT 4.

CAT 4 ticket sales $=125\times 148=18500$

1. Form the time expression using total number of people divided by evacuation rate.

$\text{Time taken}=\frac{\text{number of people}}{\text{rate}}=\frac{300}{x}$

1. Express entrance B's evacuation rate and hence form the time expression.

Entrance F evacuates $x$ people per second.

Since entrance F lets $2$ more people evacuate per second than entrance B,
$\text{rate of B}=x-2\text{ people per second}.$

Time taken using only B:
$\frac{300}{x-2}\text{ s}$

1. Factorise the quadratic expression.

$x^2-2x-200=0$
Find two numbers with product $-200$ and sum $-2$: $-20$ and $10$.
$x^2-2x-200=(x-20)(x+10)$
So,
$(x-20)(x+10)=0$

2. Solve using the zero product property.

$(x-20)(x+10)=0$
Hence,
$x-20=0 \quad \text{or} \quad x+10=0$
$x=20 \quad \text{or} \quad x=-10$

1. Select the valid evacuation rate for entrance F from the solutions of the quadratic equation.

From 7(b)(iv), $x=20$ or $x=-10$.

Since $x$ is the number of people evacuated per second, $x$ must be positive.

So, $x=20$.

2. Find the number evacuated in 1 minute by multiplying rate by time.

$1$ minute $=60$ seconds.

Number evacuated by entrance F
$=20\times 60=1200$