Higher June 2018 Paper 2 Q7
7. Alpha Bathrooms sells only one size of shower curtain and one size of rail.
Sunita is buying shower curtains and rails for her guest house.
She needs more shower curtains than rails.
6 shower curtains and 3 rails would cost her £24.60.
5 shower curtains and 2 rails would cost her £18.60.
Calculate how much change Sunita would get from £40 when buying 7 shower curtains and 5 rails.
You must use an algebraic method. [6]
| Scheme | Marks | Comments |
|---|---|---|
| \(6c + 3r = 24(.)60\) AND \(5c + 2r = 18(.)60\) | B1 | Both equations given, \(c\) & \(r\) may be other letters, words are accepted |
| Method to solve simultaneous equations, allow an error but not in the equated variable with an attempt to subtract | M1 | FT provided at least one equation is correct and consistent place value, with equivalent level of difficulty Allow 1 error in one term, not one with equal coefficients |
| First variable correct | A1 | Accept in £ or p Curtain £2.20 Rail £3.80 |
| Method to calculate second variable | m1 | FT their first variable provided M1 previously awarded |
| Second variable correct | A1 | Accept in £ or p |
| \((40 - (7c+5r) = 40 - 34.40 =)\) (£)5.6(0) or 560(p) | B1 | FT ‘their \(c\)’ and ‘their \(r\)’ provided M1 previously awarded If units are given they must be correct Unsupported answers, no marks |
| (6) |