Question

Based on past concerts, a band predicts selling 600-10p concert tickets when each ticket is sold at p dollars. Complete the table to find out how many concert tickets the band expects to sell and what revenues it expects to receive at the given ticket prices.

Answer 1

The formula for the number of tickets sold, 600 - 10·p, gives the

revenue at a given number of tickets as 600·p - 10·p².

How can the given table be completed?

The number of tickets sold = 600 - 10·p

The revenue = Ticket price × (600 - 10·p)

The completed table is presented as follows;

$\begin{array}{c|c|c|}Ticket \ price \ (dollars)&Number \ of \ tickets&Revenue \ (dollars)\\10&600 - 10 \times 10 = 500&10 \times 500 = 5000\\15&600 - 10 \times 15 = 450&10\times 450 = 4500\\20&600 - 10 \times 20 = 400&10 \times 400 = 4000\\30&600 - 10 \times 30 = 300&10 \times 300 = 3000\\35&600 - 10 \times 35 = 250&10 \times 250 = 2500\\45&600 - 10 \times 45 = 150&10 \times 150 = 1500\\50&600 - 10 \times 50 = 100&10 \times 100 = 1000\\60&600 - 10 \times 60 =0&10 \times 0 = 0\\p\end{array}\right]$

The general formula for the revenue, given a number of tickets sold of 600 - 10·p is therefore;

• The revenue = p × (600 - 10·p) = 600·p - 10·p²

Therefore, when the ticket sold is p, we have;

• Number of ticket sold = 600 - 10·p

• Revenue = 600·p - 10·p²

Learn more about functions here:

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