Higher June 2024 Paper 1 Q14
14 4 chocolate bars and 3 packets of mints cost £4.70
5 chocolate bars and 1 packet of mints cost £4.50
Work out the cost of a chocolate bar and the cost of a packet of mints. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: elimination | ||
| at least one correct equation | M1 | eg \(4x + 3y = 4.7(0)\) or \(5x + y = 4.5(0)\) or \(15x + 3y = 13.5(0)\) or \(9x + 4y = 9.2(0)\) may work in pounds or pence any letters |
| correctly multiplies one or two correct equations to equate coefficients of \(x\) or \(y\) | M1dep | eg \(4x + 3y = 4.7(0)\) and \(15x + 3y = 13.5(0)\) or \(20x + 15y = 23.5(0)\) and \(20x + 4y = 18.(00)\) |
| correctly adds or subtracts correct equations to eliminate one variable | M1dep | eg \(11x = 8.8(0)\) or \(11y = 5.5(0)\) may be implied by one correct value of \(x\) or \(y\) with M2 scored |
| chocolate bar £0.80 and packet of mints £0.50 or chocolate bar 80p and packet of mints 50p | A1 | correct money notation condone £0.80p and £0.50p |
| Alternative method 2: substitution | ||
| \(4x + 3y = 4.7(0)\) or \(5x + y = 4.5(0)\) or \(15x + 3y = 13.5(0)\) or \(9x + 4y = 9.2(0)\) | M1 | oe may work in pounds or pence any letters |
| correctly makes \(x\) or \(y\) the subject of a correct equation | M1dep | eg \(x = \dfrac{4.7(0) - 3y}{4}\) or \(x = \dfrac{4.5(0) - y}{5}\) or \(y = \dfrac{4.7(0) - 4x}{3}\) or \(y = 4.5(0) - 5x\) |
| correctly substitutes to eliminate a variable | M1dep | eg \(5\dfrac{(4.7(0) - 3y)}{4} + y = 4.5(0)\) or \(4\dfrac{(4.5(0) - y)}{5} + 3y = 4.7(0)\) or \(5x + \dfrac{4.7(0) - 4x}{3} = 4.5(0)\) or \(4x + 3(4.5(0) - 5x) = 4.7(0)\) may be implied by one correct value of \(x\) or \(y\) with M2 scored |
| chocolate bar £0.80 and packet of mints £0.50 or chocolate bar 80p and packet of mints 50p | A1 | correct money notation condone £0.80p and £0.50p |
Additional guidance
| Up to M3 may be awarded for correct work with no answer or incorrect answer if this is seen amongst multiple attempts | |
| Condone multiple letters in equations eg \(cb\) for \(x\) | |
| Trial and improvement is 0, 3 (incorrect money notation) or 4 (fully correct) | |
| Final answer chocolate bar £0.8 and packet of mints £0.5 | M3A0 |
| Final answer chocolate bar 0.80p and packet of mints 0.50p | M3A0 |