Higher November 2023 Paper 3 Q22
22 Ebony makes some bracelets to sell.
The materials to make all the bracelets cost £190, correct to the nearest £5
Ebony sells all the bracelets for a total of £875, correct to the nearest £5
The total time taken to make and sell all these bracelets was 72 hours, correct to the nearest hour.
Ebony uses this method to calculate her hourly rate of pay
\[\text{Hourly rate of pay} = \frac{\text{total selling price} - \text{total cost of materials}}{\text{total time taken}}\]The minimum hourly rate of pay for someone of Ebony’s age is £8.20
By considering bounds, determine if Ebony’s hourly rate of pay was definitely more than £8.20
You must show all your working. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| (£)9.37(9…) and conclusion | B1 | for stating at least one bound 187.5 or 192.5 or 192.499… or 872.5 or 877.5 or 877.499… or 71.5 or 72.5 or 72.499… |
| P1 | for correct use of LB and UB find the lower bound for profit, eg [LB of selling price] – [UB of costs] \((= 872.5 - 192.5\ (= 680))\) | |
| P1 | (dep P1) for correct use of LB and UB to find the lower bound for hourly rate, eg [LB of profit] ÷ [UB of hours] | |
| C1 | for (£)9.37(9…) and conclusion that Ebony does earn more than minimum wage with value from working with correct bounds |
Additional guidance
May be seen in calculations
Accept 192.499... or \(192.4\dot{9}\) or 877.499... \(877.4\dot{9}\) or 72.499… or \(72.4\dot{9}\)
\(872.5 \leqslant [\text{LB selling price}] \lt 875\)
\(190 \lt [\text{UB costs}] \leqslant 192.5\)
LB profit = "680"
\(72 \lt [\text{UB hours}] \leqslant 72.5\)
\(\dfrac{872.5 - 192.5}{72.5}\)
Accept bounds truncated or rounded to at least 2 dp