Higher November 2021 Paper 3 Q14
14 Olivia and Jessica have in total half as many sweets as Fran and Gary have in total.
Fran and Gary share their sweets in the ratio \(2 : 3\)
Olivia and Jessica share their sweets in the ratio \(9 : 1\)
Fran got \(w\) sweets.
Gary got \(x\) sweets.
Olivia got \(y\) sweets.
Jessica got \(z\) sweets.
Find, in its simplest form, \(w : x : y : z\) (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 8 : 12 : 9 : 1 | P1 | for \(2 + 3\ (= 5)\) and \(9 + 1\ (= 10)\) OR for assigning a total number of sweets for F + G and O + J eg F + G = 100, O + J = 50 |
| P1 | for finding correct multiplier for relationship between totals for F + G and O + J eg \(\times 4\) to get from 5, 10 to 20, 10 OR for working out the number of sweets from their totals for F, G eg 40, 60 or for O, J, eg 45, 5 | |
| P1 | for \(2 \times 4\ (= 8)\) and \(3 \times 4\ (= 12)\) OR for ratio in unsimplified form, eg 40 : 60 : 45 : 5 | |
| A1 | cao |
Additional guidance
May be in algebraic form, eg \(2a + 3a\ (= 5a)\) and \(9a + 1a\ (= 10a)\)
May be in algebraic form, eg F + G = \(5a\), O + J = \(2.5a\)