Question

At a Youth Festival concert, the ratio of the number of Chinese to that of Malays was 8:7. The ratio of the number of Malays to that of Indians was 5:4.
a) Find the ratio of the number of Chinese to the number of Malays to the number of Indians.
b) After 39 Indians left the concert, 1/6 of the remaining audience at the concert were Indians. Find the total number of Chinese and Indians at the concert at first.

Answer 1

C : M = 8 : 7 = 40 : 35
M : I = 5:4 = 35 : 28

a)
C : M : I = 40 : 35 : 28

b) total at concert = 40x + 35x + 28x = 103x

number of Indians = 28x
after 39 left, number of Indians = 28x - 39
number left at concert = 103x - 39

28x - 39 = (1/6)(103x - 39)
168x - 234 = 103x - 39
65x = 195
x = 3

so
C = 120
M = 105
I = 84, for a total of 309

after departure: Indians --- 45
total after departure = 309-39 = 270

45/270 = 1/6, YEAHH!

Answer 2

C:M = 8:7 = 40:35
M:I = 5:4 = 35:28
C:M:I = 40:35:28
so, C:M = 40:35 = 8:7

I-39 = 1/6 (C+M+I-39)
I-39 = 1/6 (10/7 I + 5/4 I + I - 39)
I = 84
C = 10/7 * 84 = 120
so, 120+84 = 204