Higher June 2018 Paper 1 Q8
8. Jamil is taking a group of students on a camping trip.
(a) He buys tins of soup and bottles of water.
He needs to buy the same number of tins as bottles.
Tins of soup are sold in packs of 12 and bottles of water are sold in packs of 15.
He needs to buy the same number of tins as bottles.
Tins of soup are sold in packs of 12 and bottles of water are sold in packs of 15.
What is the smallest number of packs of each that Jamil can buy? [2]
Number of packs of soup ………… Number of packs of water …………
(b) Jamil buys packs of sausages and packs of burgers for the trip in the ratio 3 : 4.
The cost of a pack of sausages is 75% of the cost of a pack of burgers.
Jamil buys 16 packs of burgers.
Each pack of burgers costs £\(x\).
He spends £125 in total.
The cost of a pack of sausages is 75% of the cost of a pack of burgers.
Jamil buys 16 packs of burgers.
Each pack of burgers costs £\(x\).
He spends £125 in total.
How much does Jamil pay for each pack of sausages? [4]
Each pack of sausages costs £ …………
| Scheme | Marks | Comments |
|---|---|---|
| (soup =) 5 (water = ) 4 | B2 | B1 for sight of 3 × 4 and 3 × 5 or equivalent or for (LCM =) 60 or for a correct Venn diagram of primes factors or for answers of \(5n\) and \(4n\) where \(n\) is an integer > 1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(12\times\tfrac34x+16\times x\ (=125)\) or equivalent, seen or implied | M2 | implied by 12 × 3.75 + 16 × 5 = 125 from trials or costs in the ratio 9 : 16 seen or implied M1 for (pack of sausages cost) \(\tfrac34x\) or equivalent or for sight of (packs of sausages =) 12 or for ‘their 12’ × ‘their \(\tfrac34x\)’ \(+\,16\times x=125\), provided ‘their \(x\)’ \(\ne 1\) |
| \((x =)\ 5\) or equivalent, seen or implied | A1 | CAO |
| £3.75 | B1 | FT ¾ of ‘their 5’ or equivalent, provided ‘their 5’ is not an integer multiple of 4 |
| (6) |