Higher June 2022 Paper 1 Q13
13 Antoine is going on holiday.
He makes 3 separate payments to cover the total cost of his holiday.
The following table shows how much money Antoine pays to the holiday company.
| Payment | Amount paid |
|---|---|
| Payment 1 | \(\dfrac{3}{8}\) of the total cost |
| Payment 2 | 45% of the total cost |
| Payment 3 | $406 |
Work out how much Antoine has to pay for Payment 2
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{8} + 45\%\left(= \dfrac{33}{40} \text{ or } 82.5(\%) \text{ or } 0.825\right)\) | M1 |
\(1 - \text{``}{\dfrac{33}{40}}\text{''}\left(= \dfrac{7}{40}\right)\) or \(100 - \text{``}{82.5}\text{''}(\%)\;(= 17.5(\%))\) or \(1 - \text{``}{0.825}\text{''}\;(= 0.175)\) | M1 |
\(406 \div \text{``}{\dfrac{7}{40}}\text{''}\) (= 2320) or \(406 \div \dfrac{\text{``}{17.5}\text{''}}{100}\) oe (= 2320) or 1% = 406 ÷ “17.5” (= 23.2) oe | M1 |
| 0.45 × “2320” oe or 45 × “23.2” oe | M1 |
| 1044 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: Do NOT award M1 for e.g.
\(\dfrac{3}{8} + 45(\%) + 406\;(= \ldots.)\) oe
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{8}x + 0.45x + 406\) oe | M1 |
| \(\dfrac{3}{8}x + 0.45x + 406 = x\) oe | M1 |
| \((x =)\;\dfrac{406}{1 - \dfrac{3}{8} - 0.45}\left(= \dfrac{406}{7/40} = 2320\right)\) | M1 |
| 0.45 × “2320” | M1 |
| 1044 | A1 |
Notes
M1: Do NOT award M1 for e.g.
\(\dfrac{3}{8} + 45(\%) + 406\;(= \ldots.)\) oe
M1: for a correct equation