# 04 - In a Mixed Company of ASEAN Nationalities

**Problem**

In a mixed company of Malaysians, Vietnamese, Singaporeans, Thais, and Filipinos, the Malaysians are one less than 1/3 of the Filipinos; and three less than half the Vietnamese. The Filipinos and Thais outnumber the Singaporeans and Vietnamese by 3. The Singaporeans and Filipinos form one less than half the company, and the Singaporeans and Vietnamese form 7/16 of the company. How many persons of each nationality were there?

**Answer Key**

**Solution**

$M = \frac{1}{3}F - 1$

$F = 3M + 3$ ← Equation (1)

...and three less than half the Vietnamese

$M = \frac{1}{2}V - 3$

$V = 2M + 6$ ← Equation (2)

The Filipinos and Thais outnumber the Singaporeans and Vietnamese by 3

$(F + T) - (S + V) = 3$

$F + T - S - V = 3$ ← Equation (3)

The Singaporeans and Filipinos form one less than half the company

$S + F = \frac{1}{2}(M + V + S + T + F) - 1$

$M + V - S + T - F = 2$ ← Equation (4)

...the Singaporeans and Vietnamese form 7/16 of the company

$S + V = \frac{7}{16}(M + V + S + T + F)$

$7M - 9V - 9S + 7T + 7F = 0$ ← Equation (5)

Equation (3) - Equation (4)

$2F - 2V - M = 1$ ← Equation (6)

Substitute *F* of Equation (1) and *V* of Equation (2) to Equation (6)

$2(3M + 3) - 2(2M + 6) - M = 1$

$M = 7$

From Equation (1)

$F = 3(7) + 3$

$F = 24$

From Equation (2)

$V = 2(7) + 6$

$V = 20$

From Equation (3)

$24 + T - S - 20 = 3$

$T = S - 1$ ← Equation (7)

From Equation (5)

$7(7) - 9(20) - 9S + 7(S - 1) + 7(24) = 0$

$2S = 30$

$S = 15$

From Equation (7)

$T = 15 - 1$

$T = 14$

Summary:

Vietnamese = 20

Singaporeans = 15

Thais = 14

Filipinos = 24

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