The seats in a cinema are divided into three sections. There is one central section and two aisle sections. The central section consists of 12 rows of 18 seats. 21 27ths of the central seats have been booked for a given show. The two aisle sections each consist of 12 rows of seven seats. Seven 12ths of the aisle seats have been booked for the same show. Are more than a quarter of seats still available? You must show your working.
Let’s firstly calculate the total number of seats in the cinema. We’re told that the central section consists of 12 rows of 18 seats. Therefore, the total number of seats is 12 multiplied by 18. This is equal to 216. So there are 216 seats in the central section. The two aisle sections each consists of 12 rows of seven seats. Therefore, the number of seats in each aisle section is 12 multiplied by seven. As there are a two of these sections, we need to multiply this answer by two. 12 multiplied by seven is equal to 84. Multiplying this by two gives us 168. We can calculate the total number of seats in the cinema by adding 168 and 216. This is equal to 384.
We’re also told that 21 27ths of the central seats have been booked for a given show. We need to calculate 21 27ths of 216. The word “of” in mathematics means multiply. So we need to multiply the fraction by 216. This gives us an answer of 168. Therefore, 168 of the central seats have been booked. We’re also told that seven 12ths of the aisle seats have been booked. As there were 168 aisle seats in total, we need to work out seven 12ths multiplied by 168. This is equal to 98. We can calculate the total number of seats that have been booked for the show by adding 168 to 98. This is equal to 266.
We were asked to work out whether more than a quarter of the seats are still available. Firstly, we can work out one-quarter of 384 as there were 384 seats in total. One-quarter multiplied by 384 is 96. We know that 266 out of the 384 seats have been booked. Therefore, the number of seats remaining can be calculated by subtracting 266 from 384. This is equal to 118. 118 is greater than 96. We can therefore conclude yes, there are more than one-quarter of seats still available.
In any question like this, we must give a reason in our answer. In this case, it is the fact that 118 — the number of seats — remaining is greater than 96, one-quarter of the seats.