At the supermarket, Ben buys 5 apples and 3 pears, at a total cost of £3.70. Jenny buys 6 apples and 6 pears, costing £5.40. Construct two simultaneous equations to work out the price, in pence, of apples and pears.

Ben: 5 apples and 3 pears costing £3.70, therefore: 5a + 3p = 3.7. Jenny: 6 apples and 6 pears costing £5.40, therefore: 6a + 6p = 5.4. (1) 5a + 3p = 3.7, (2) 6a + 6p = 5.4. Multiply equation (1) by 2: 10a + 6p = 7.4; 6a + 6p = 5.4. Make 6p the subject of the equation: 6p = 7.4 - 10a; 6p = 5.4 - 6a. Equate and solve: 7.4 - 10a = 5.4 - 6a, 7.4 - 5.4 = -6a + 10a, 2 = 4a, therefore: a = 2/4 = 0.5. Place a = 0.5 into equation (1). 5(0.5) + 3p = 3.7, 2.5 + 3p = 3.7, 3p = 3.7 - 2.5, 3p = 1.2, therefore: p = 1.2/3 = 0.4. Place a = 0.5 and p = 0.4 into equation (2) to check answer: 6(0.5) + 6(0.4) = 5.4, 3 + 2.4 = 5.4, 5.4 = 5.4. Therefore: a = £0.5 = 50p, p = £0.4 = 40p. ANSWER: At the supermarket, apples cost 50p and pears cost 40p.