2x/3 = 3y/5 = 5z/4 = k -> coeficient de proportionalitate
2x/3 = k => x = 3k/2
3y/5 = k => y = 5k/3
5z/4 = k => z = 4k/5
x + y + z = 1
3k/2 + 5k/3 + 4k/5 = 1 l × 30 ( c.m.m.m.c al numitorilor 2, 3 si 5 = 30 )
15 × 3 k + 10 × 5 k + 6 × 4 k = 30
45 k + 50 k + 24 k = 30
119 k = 30
k = 30/119
x = 3 · 30/119 × ( 1/2) => x = 45/119
y = 5 ·30/119 × ( 1/3) ⇒ y = 50/119
z = 4 × 30/119 × ( 1/5) => z = 24/119
x + y + z = 45/119 + 50/119 + 24/119 = 119/119 = 1
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