Numeracy Intermediate November 2016 Unit 1 Q9
9.
(a) Lotty and Rafael decide to enter a prize draw.
They agree to share any money they win in the ratio 2 : 3 respectively.
After winning a total of £2000, they think again and decide that Lotty’s share should be increased by 30%.
They agree to share any money they win in the ratio 2 : 3 respectively.
After winning a total of £2000, they think again and decide that Lotty’s share should be increased by 30%.
(i) Rafael thinks that his share will be reduced by 30%.
Without any calculation, explain why Rafael’s thinking is incorrect. [1]
Without any calculation, explain why Rafael’s thinking is incorrect. [1]
(ii) Calculate the amount of money Lotty wins after the decision is made to increase her share. [4]
(iii) Find the ratio that is now used to share the money between Lotty and Rafael.
Express your answer in its simplest form. [3]
Express your answer in its simplest form. [3]
Lotty’s winnings : Rafael’s winnings = ………… : …………
(b) In another prize draw, it was planned to give £5000 as the first prize.
To make it more popular, the organisers decide to increase this first prize by 26%.
To make it more popular, the organisers decide to increase this first prize by 26%.
The most efficient method of calculating the amount of the increased first prize is
1·26 × 5000.
The second prize was planned to be £3000, but it is now decided to decrease this prize by 6%.
Write down the most efficient method of calculating the amount of the decreased second prize.
You are not expected to work out the answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| (i) Reason, e.g. ‘because it is not 30% less than the original amount’, ‘it is 30% less of a different amount’, ‘30% for Lotty is not the same as 30% for Rafael’, ‘30% of his share is more than 30% of her share’, ‘it would be 30% of Lotty’s winnings so it would not be 30% of Rafael’s total winnings’, ‘Lotty’s share will increase by 30% not by the percentage of his amount’ | E1 | Ignore additional spurious comments Allow a correct reason ignoring calculations provided the reason is not based on calculations Allow ‘they do not get the same amount of money to begin with’, ‘because Rafael has 3 of the ratio when Lotty has the total of 2’, ‘because Rafael gets a higher ratio than Lotty’ Do not accept ‘this is because the shares wouldn’t be even’, ‘because Rafael will get more than Lotty’, ‘he would get 30% less’ |
| (ii) 2000 × 2 ÷ 5 or equivalent | M1 | |
| × 1.3(0) or equivalent | M1 | |
| (£) 1040 | A2 | A1 for intermediate answers of (£) 800 or (£)2600 |
| (iii) (Rafael now wins 2000 – 1040) (£) 960 | B1 | FT 2000 - ‘their 1040’ provided both previous M marks awarded This mark may be implied in further working |
| New ratio fully simplified 13 : 12 | B2 | B1 for new ratio (1040 : 960) with at least one step of simplification, e.g. 104 : 96, 520 : 480 FT provided equivalent difficulty, award B1 only if only 1 common factor in the simplification, or B1 for 12 : 13 given in the answer space |
| Scheme | Marks | Comments |
|---|---|---|
| 0.94 × 3000 | B1 | Allow 3000 × 94/100 Do not accept 3000 – 0.06 × 3000 |