Higher June 2022 Paper 2 Q7
7 In Spain, Sam pays 27 euros for 18 litres of petrol.
In Wales, Leo pays £40.80 for 8 gallons of the same type of petrol.
1 euro = £0.85
4.5 litres = 1 gallon
Sam thinks that petrol is cheaper in Spain than in Wales.
Is Sam correct?
You must show how you get your answer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| No (supported) | P1 | for a conversion with litres and gallons, eg \(18 \div 4.5\ (= 4)\) or \(8 \times 4.5\ (= 36)\) |
| P1 | for a conversion with £ and euros, eg \(27 \times 0.85\ (= 22.95)\) or \(40.8 \div 0.85\ (= 48)\) | |
| P1 | for finding the unit price, eg \(27 \div 18\ (= 1.5)\) OR finding proportionality for fuel eg \((\text{``}36\text{''} \div 18)\ (= 2)\) | |
| C1 | for No with comparative figures, eg No with 20.4 and 22.95 OR No with 1.275 and 1.133… |
Additional guidance
See additional information below
May compare cost per gallon or cost in euros
May be seen in a calculation or given in a description
Accept comparative figures rounded or truncated
No is implied by eg Wales is cheaper
Question 7 – Additional information NOT Exhaustive
Cost per litre in £:
\(27 \times 0.85\ (= 22.95)\)
\(\text{``}22.95\text{''} \div 18\ (= 1.275)\)
\(8 \times 4.5\ (= 36)\)
No and \(40.8 \div \text{``}36\text{''} = 1.133..\) (cost per litre in £ in Wales) compared to 1.275 (cost per litre in £ in Spain).
Cost per litre in euros:
\(27 \div 18\ (= 1.5)\)
\(8 \times 4.5\ (= 36)\)
\(40.8 \div 0.85\ (= 48)\)
No and \(\text{``}48\text{''} \div \text{``}36\text{''} = 1.333..\) (cost per litre in euros in Wales) compared to 1.5 (cost per litre in euros in Spain).
Cost per gallon in £:
\(40.8 \div 8\ (= 5.1)\)
\(27 \times 0.85\ (= 22.95)\)
\(18 \div 4.5\ (= 4)\)
No and \(\text{``}22.95\text{''} \div \text{``}4\text{''} = 5.7375\) (cost per gallon in £ in Spain) compared to 5.1(0) (cost per gallon in £ in Wales).
Cost per gallon in euros:
\(40.8 \div 0.85\ (= 48)\)
\(\text{``}48\text{''} \div 8\ (= 6)\)
\(18 \div 4.5\ (= 4)\)
No and \(27 \div \text{``}4\text{''} = 6.75\) (cost per gallon in euros in Spain) compared to 6 (cost per gallon in euros in Wales).
Note: “2” comes from \(8 \div \text{``}4\text{''}\) or \(\text{``}36\text{''} \div 18\)
Cost of 8 gallons in £:
\(18 \div 4.5\ (= 4)\)
\(27 \times 0.85\ (= 22.95)\)
\(\text{``}22.95\text{''} \times \text{``}2\text{''}\ (= 45.90)\)
No and 45.90 (total cost in £ in Spain) compared to 40.80 (total cost in £ in Wales given).
Cost of 8 gallons in euros:
\(18 \div 4.5\ (= 4)\)
\(40.8 \div 0.85\ (= 48)\)
\(27 \times \text{``}2\text{''}\ (= 54)\)
No and 54 (cost for 8 gallons in euros in Spain) compared to 48 (cost of 8 gallons in euros in Wales).
Cost of 18 litres in £:
\(8 \times 4.5\ (= 36)\)
\(40.8 \div \text{``}2\text{''}\ (= 20.4)\)
\(27 \times 0.85\ (= 22.95)\)
No and 22.95 (cost for 18 litres in £ in Spain) compared to 20.40 (cost of 18 litres in £ in Wales).
OR
\(18 \div 4.5\ (= 4)\)
\(27 \times 0.85\ (= 22.95)\)
\(40.8 \div \text{``}2\text{''}\ (= 20.4)\)
No and 22.95 (cost for 18 litres in £ in Spain) compared to 20.40 (cost of 18 litres in £ in Wales).
Cost of 18 litres in euros:
\(18 \div 4.5\ (= 4)\)
\(40.8 \div 0.85\ (= 48)\)
\(\text{``}48\text{''} \div \text{``}2\text{''}\ (= 24)\)
No and 24 (cost for 18 litres in euros in Wales) compared to 27 (cost of 18 litres in euros in Spain given).
OR
\(8 \times 4.5\ (= 36)\)
\(40.8 \div \text{``}2\text{''}\ (= 20.4)\)
\(\text{``}20.4\text{''} \div 0.85\ (= 24)\)
No and 24 (cost for 18 litres in euros in Wales) compared to 27 (cost of 18 litres in euros in Spain given).