...the Malaysians are one less than 1/3 of the Filipinos
$M = \frac{1}{3}F - 1$
$F = 3M + 3$ ← 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:
Malaysians = 7
Vietnamese = 20
Singaporeans = 15
Thais = 14
Filipinos = 24
