Foundation November 2024 Paper 3 Q14
14
(a) Machine A makes enough lollipops to fill 300 packs.
There are 8 lollipops in each pack.
There are 8 lollipops in each pack.
Show that 2400 lollipops are made by machine A. [1]
(b) Machine B makes 3600 lollipops in the same time it took by machine A to make 2400 lollipops.
Machine B makes lollipops one at a time and at a constant rate.
Machine B makes lollipops one at a time and at a constant rate.
What fraction of the time needed to fill 300 packs is saved if machine B is used rather than machine A?
Give your answer in its simplest form. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(300 \times 8\) [= 2400] | 1 | Condone also doing the reverse \(2400 \div 8\) or \(2400 \div 300\) as a check | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{1}{3}\) | 3 | B2 for \(\dfrac{1200}{3600}\) oe or M2 for \(1 - \dfrac{2400}{3600}\) oe or B1 for \(\dfrac{2400}{3600}\) oe or \(\dfrac{3600}{2400}\) oe or 1200 | May be \(\dfrac{3600}{1200}\) oe Answers of 33.3[3...]% or 0.333[3...] or 3 score B2 May be \(1 - \dfrac{1}{1.5}\) or \(1 - \dfrac{x}{1.5x}\) or \(\dfrac{3600 - 2400}{3600}\) etc e.g. \(\dfrac{2}{3}\) or \(\dfrac{3}{2}\) 66% to 67% or 0.66 to 0.67 or \(\dfrac{300}{450}\) or 1.5 A time may be chosen e.g. 1 hour 3600 in 60 min, 60 per min 2400 in 60 min, 40 per min B1 for \(\dfrac{40}{60}\), M2 for \(1 - \dfrac{40}{60}\) etc |