Unit 3
4 marks · Normal(a) Anna shares £136 between herself and two friends in the ratio 4 : 3 : 1. Work out how much each person receives.
(b) The ratio of the lengths of two similar rectangles is 2 : 5. If the area of the smaller rectangle is 16 cm^2, find the area of the larger rectangle.
Anna shares £136 between herself and two friends in the ratio 4 : 3 : 1. Work out how much each person receives.
If the area of the smaller rectangle is 16 cm^2, what is the area of the larger?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) £68, £51, £17 · must show 68, 51, 17
(b) 100 cm^2 · must show 100
Common mistakes: Using side ratio not area ratio; Incorrect splitting of amounts
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Adds parts to get total (8) and finds each share as a fraction of £136.
A1 (a) · 2 marks · Correct shares: £68, £51, £17.
M2 (b) · 1 mark · Squares ratio (2:5 → area ratio 4:25), multiplies 16×(25/4).
Worked solution
(a) Total parts = 4+3+1=8. Each part = 136/8=17. Anna: 4×17=£68, Friend1: 3×17=£51, Friend2: 1×17=£17.
(b) Area ratio = (2/5)^2 = 4/25 so larger area = 16×(25/4)=100 cm^2.