Higher June 2022 Paper 1 Q3
3 A delivery company has a total of 160 cars and vans.
the number of cars : the number of vans = 3 : 7
Each car and each van uses electricity or diesel or petrol.
\(\dfrac{1}{8}\) of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.
Work out the number of cars that use petrol.
You must show all your working. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 30 | P1 | for \(160 \div (3+7)\ (= 16)\) or \(\dfrac{3}{3+7}\ \left(= \dfrac{3}{10}\right)\) |
| P1 | for \(\text{``}16\text{''} \times 3\ (= 48)\) or \(\text{``}\dfrac{3}{10}\text{''} \times 160\ (= 48)\) | |
| P1 | for a correct step using 48 eg \(\text{``}48\text{''} \div 8\ (= 6)\) or \(\text{``}48\text{''} \times 25 \div 100\ (= 12)\) or (indep) for combining \(\dfrac{1}{8}\) and 25%, eg \(\dfrac{1}{8} + \dfrac{1}{4}\ \left(= \dfrac{3}{8}\right)\) or \(\text{``}0.125\text{''} + \text{``}0.25\text{''}\ (= 0.375)\) or “12.5”(%) + 25(%) (= 37.5(%)) | |
| P1 | for a complete process to find the number of petrol cars, eg \(\text{``}48\text{''} - \text{``}6\text{''} - \text{``}12\text{''}\) oe or \(\left(1 - \text{``}\dfrac{3}{8}\text{''}\right) \times \text{``}48\text{''}\) oe or \(\text{``}\dfrac{3}{10}\text{''} \times \left(1 - \text{``}\dfrac{3}{8}\text{''}\right) \times 160\) oe | |
| A1 | cao SC B2 for an answer of 100 if P0 scored |
Additional guidance
Award no marks for a correct answer with no supportive working