Foundation June 2018 Paper 2 Q26
26 Theo starts with savings of £18
James starts with no savings.
Each week from now,
Theo will save £4.50 and James will save £4
In how many weeks will Theo and James have savings in the ratio 15 : 8 ? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| 22.5(0) and 4 or 27 and 8 or 31.5(0) and 12 or 36 and 16 or 40.5(0) and 20 or 45 and 24 or 30 : 16 or 45 : 24 | M1 | |
| 45 and 24 chosen | A1 | eg 45 : 24 is the final ratio seen |
| 6 | A1 | |
| Alternative method 2 | ||
| \(18 + 4.5x\) and \(4x\) seen or \(\dfrac{18 + 4.5x}{15} = \dfrac{4x}{8}\) | M1 | any letter oe sets up correct equation |
| \(8(18 + 4.5x) = 60x\) or \(144 + 36x = 60x\) or \(24x = 144\) | M1dep | eliminates denominators oe |
| 6 | A1 | |
Additional guidance
| Answer 6 that is not from incorrect method | M1A1A1 |
| 45 and 24 followed by eg 49.5(0) and 28 (answer not 6) | M1A0A0 |
| Equivalent ratio to 15 : 8 that is not 30 : 16 or 45 : 24 eg 60 : 32 (answer not 6) | M0A0A0 |
| Final calculation \(\dfrac{15}{8} \times 24 = 45\) (answer not 6) | M1A1A0 |