Higher June 2023 Paper 3 Q8

8 Jing has £2450

She saves some and gives the rest to her four brothers.

money saved : money given to brothers = 2 : 5

She gives each of her four brothers the same amount.

Does each brother receive more than £430 ?

You must show your working. [4 marks]

Mark scheme

Answer	Mark	Comments
Alternative method 1
\(2450 \div (2 + 5)\) or \(2450 \div 7\) or 350	M1	oe
their \(350 \times 5\) or 1750 or their \(350 \times 2\) or 700 or their \(350 \div 4\) or 87.5(0)	M1dep	oe \(2450 \times \dfrac{5}{7}\) is M2 \(2450 \times \dfrac{2}{7}\) is M2 \(2450 \div 28\) is M2
their \(1750 \div 4\) or \((2450 -\) their \(700) \div 4\) or their \(87.5(0) \times 5\) or 437.5(0)	M1dep	oe dep on M2 \(350 \times \dfrac{5}{4}\) is M3
437.5(0) and Yes	A1	accept \(437.5(0) \gt 430\)
Alternative method 2
\(2450 \div 4\) or 612.5(0)	M1	oe
their \(612.5(0) \div (2 + 5)\) or their \(612.5(0) \div 7\) or 87.5(0)	M1dep	oe \(2450 \div 28\) is M2
their \(87.5(0) \times 5\) or their \(612.5(0) -\) their \(87.5(0) \times 2\) or 437.5(0)	M1dep	oe dep on M2 \(612.5(0) \times \dfrac{5}{7}\) is M3
437.5(0) and Yes	A1	accept \(437.5(0) \gt 430\)
Alternative method 3
\(430 \times 4\) or 1720	M1
\(2450 \div (2 + 5)\) or \(2450 \div 7\) or 350	M1	oe
their \(350 \times 5\) or 1750 or their \(350 \times 2\) or 700	M1dep	oe dep on 2nd M \(2450 \times \dfrac{5}{7}\) is M2 \(2450 \times \dfrac{2}{7}\) is M2
1720 and 1750 and Yes	A1	\(2450 - 1720 = 730\) and 700 and Yes
Alternative method 4
\(430 \times 4\) or 1720	M1
their \(1720 \div 5\) or 344 or their \(1720 \times 2\) or 3440	M1dep	oe
their \(344 \times 2\) or their \(3440 \div 5\) or 688	M1dep	oe dep on M2 \(1720 \times \dfrac{2}{5}\) is M3
2408 and Yes	A1

Up to M3 may be awarded for correct work, with no answer or incorrect answer, even if this is seen amongst multiple attempts
\(2450 \div 7 \times 1.25\) or \(350 \times 1.25\)	M1M1M1
Yes may be implied eg They receive 7.50 more than 430	M3A1
Condone £437.50p and Yes	M3A1