Answer:
the value of p is £3.67.
Explanation:
(a) To determine the value of p, we need to use the information given in the problem to set up and solve a simple equation. The cost of the repair at one house was £71, and it took 3 hours, so the cost per hour was £71 / 3 = £<<71/3=23.67>>23.67 per hour. The engineer charges £20 plus £p per hour, so £23.67 per hour is equal to £20 + £p. Subtracting £20 from both sides gives us £p = £3.67. Therefore, the value of p is £3.67.
(b) The formula for the cost, £C, of a repair that takes x hours can be written as: £C = £20 + (£p * x). This formula states that the cost of the repair is equal to the fixed cost of £20, plus the cost per hour (£p) multiplied by the number of hours (x) that the repair takes.
(c) To determine how long a repair that costs £96.50 takes, we can use the formula from part (b) and solve for x. Substituting in the known values, we get: £96.50 = £20 + (£3.67 * x). Subtracting £20 from both sides gives us: £76.50 = (£3.67 * x). Dividing both sides by £3.67 gives us: x = 20.89 hours.