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