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Question 7

The pop group Third Dimension performed a concert at the O_3 Arena. There were three grades of seats available:

- Grade A seats were the most expensive.
- Grade B seats were moderately priced.
- Grade C seats were the cheapest, costing £8.

The ratio of ticket prices was A : B : C = 3 : 2 : 1.

(a) What is the price of each type of seat?


Sagot :

To determine the price of each type of seat, we will follow the given ratio between the prices of the different grades of seats. The ratio is:

Grade A : Grade B : Grade C = 3 : 2 : 1

We also know that the cheapest seats, Grade C, are priced at £8.

Given that the ratio of ticket prices expresses the relationship between the different prices, we can determine the actual prices as follows:

1. Price of Grade C Seats (Cheapest):
We are already informed that the price of Grade C seats is £8.

2. Price of Grade B Seats (Middle Price):
According to the ratio, Grade B seats are twice the price of Grade C seats.
Therefore:
[tex]\[ \text{Price of Grade B seats} = 2 \times \text{Price of Grade C seats} = 2 \times 8 = £16 \][/tex]

3. Price of Grade A Seats (Most Expensive):
Similarly, the ratio shows that Grade A seats are three times the price of Grade C seats.
Therefore:
[tex]\[ \text{Price of Grade A seats} = 3 \times \text{Price of Grade C seats} = 3 \times 8 = £24 \][/tex]

In summary, the prices for each type of seat are:

- Grade A seats: £24
- Grade B seats: £16
- Grade C seats: £8
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