Higher June 2017 Paper 2 Q2
2 On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 5 : 2
Each person had a seat in the Circle or had a seat in the Stalls.
\(\dfrac{3}{4}\) of the children had seats in the Stalls.
117 children had seats in the Circle.
There are exactly 2600 seats in the theatre.
On this Saturday, were there people on more than 60% of the seats?
You must show how you get your answer. (5)
| Answer | Mark | Notes |
|---|---|---|
| Yes (supported) | P1 | for process to work out the total number of children, e.g. \(117 \times 4\ (= 468)\) |
| P1 | (dep P1) for process to work out total number of adults or the total number of people, e.g. \(\text{``}468\text{''} \times 5 \div 2\ (= 1170)\) or \(\text{``}468\text{''} \times 7 \div 2\ (= 1638)\) | |
| A1 | for 1170 or 1638 | |
| P1 | for process to work out the percentage of theatre full, e.g. \(\dfrac{\text{``}468\text{''} + \text{``}1170\text{''}}{2600} \times 100\ (= 63)\) or for a process to work out 60% of 2600 (= 1560) | |
| C1 | for a correct conclusion supported by correct figures e.g. 63% or 1560 and 1638 | |
| OR | ||
| P1 | for a process to work out 60% of 2600, eg. \(\dfrac{60}{100} \times 2600\ (= 1560)\) | |
| P1 | (dep P1) for process to work out this total number of children, e.g. \(\text{``}1560\text{''} \times 2 \div 7\ (= 445(.7\ldots)\) | |
| A1 | for 445(.7...) | |
| P1 | for process to work out children in the circle, eg. \(\text{``}445(.7\ldots)\text{''} \div 4\ (= 111\) to \(112)\) | |
| C1 | for a correct conclusion supported by correct figures e.g. 111 to 112 [Where appropriate, accept rounded or truncated values] | |
| OR | ||
| P1 | for a process to find the maximum number of children, eg. \(2600 \times 2 \div 7\ (= 742(.8\ldots))\) | |
| P1 | for process to work out the total number of children, e.g. \(117 \times 4\ (= 468)\) | |
| A1 | for 468 and 742(.8...) | |
| P1 | for \(\dfrac{\text{``}468\text{''}}{\text{``}742(.8..)\text{''}} \times 100\ (= 63)\) or process to work out 60% of “742.8..” (= 445(7..)) | |
| C1 | for a correct conclusion supported by correct figures e.g. 63% or 468 and 445(.7...) [Where appropriate, accept rounded or truncated values] |