Numeracy Intermediate November 2017 Unit 2 Q8
8. Handmade socks, knitted using pure cashmere wool, are very expensive to buy.
Rowena buys cashmere wool in 20 g balls.
Each ball of cashmere wool costs her £1.42.
She pays her sister £8 to knit each pair of socks.
135 g of cashmere wool is used to knit each pair of socks.
Rowena sells 40 pairs of cashmere socks for £18.95 per pair.
What is her percentage profit?
Give your answer correct to 2 significant figures.
You must show all your working. [7]
Rowena’s percentage profit when selling all 40 pairs of socks is …………… %,
correct to 2 significant figures.
| Scheme | Marks | Comments | ||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Accept rounding or truncation of 1/2p throughout | ||||||||||||||||||||||||||||||||
| (Balls of wool per pair) 135 ÷ 20 (× 40) | M1 | |||||||||||||||||||||||||||||||
| 6.75 (balls) or 7 (balls) or 270 (balls) or 280 (balls) | A1 | |||||||||||||||||||||||||||||||
| (Costs are 40 ×) 1.42 × 135 ÷ 20 (+(40 ×) 8) | m1 | FT 135 ÷ 20 = 6.75 balls and 7 balls
| ||||||||||||||||||||||||||||||
| (Profit = Sales – Costs), e.g. (Profit per pair) 18.95 - 1.42 × 135 ÷ 20 - 8 OR (Profit for 40 pairs) 40 × 18.95 – 40 × (1.42 × 135 ÷ 20 + 8) OR Appropriate amounts used to calculate (100 ×) \(\dfrac{\text{total sales}}{\text{total costs}}\) - 1 (× 100) | M2 |
M1 for any 1 of the following:
| ||||||||||||||||||||||||||||||
| Use of appropriate amounts to calculate: (Percentage profit = 100 ×) \(\dfrac{\text{profit}}{\text{costs}}\) or (100 ×) \(\dfrac{\text{sales}}{\text{costs}}\) - 1 (× 100) | m1 | FT from previous M1 or M2 FT \(\dfrac{\text{18.95 – ‘their cost per pair’}}{\text{‘their cost per pair’}}\) OR \(\dfrac{\text{40 }\times\text{ ‘their 18.95’ – ‘their total costs’}}{\text{‘their total costs’}}\) OR equivalent | ||||||||||||||||||||||||||||||
| 7.8(%) or 5.6(%) | A1 | No other FT, must be 2 s.f. 7.8% CAO comes from use of 6.75 balls, 5.6% CAO comes from use of 7 balls | ||||||||||||||||||||||||||||||
Corrected by Westie's Workshop
- The board's mark scheme printed “‘40 × ‘their 18.95’ – ‘their total costs’”. Changed to “40 × ‘their 18.95’ – ‘their total costs’” because there is a stray opening quotation mark before “40”, which is never closed.
Original: see the board's mark scheme PDF (link above).