...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