Trio ratio

Hans, Alena, and Thomas have a total of 740 USD. Hans and Alena split in the ratio of 5:6, and Alena and Thomas in the ratio of 4:5. How much will everyone get?

Correct answer:

a =  240
h =  200
t =  300

Step-by-step explanation:


h+a+t = 740
6h = 5a
5a = 4t

h+a+t = 740
6·h = 5·a
5·a = 4·t

a+h+t = 740
5a-6h = 0
5a-4t = 0

Pivot: Row 1 ↔ Row 2
5a-6h = 0
a+h+t = 740
5a-4t = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-6h = 0
2.2h+t = 740
5a-4t = 0

Row 3 - Row 1 → Row 3
5a-6h = 0
2.2h+t = 740
6h-4t = 0

Pivot: Row 2 ↔ Row 3
5a-6h = 0
6h-4t = 0
2.2h+t = 740

Row 3 - 2.2/6 · Row 2 → Row 3
5a-6h = 0
6h-4t = 0
2.467t = 740


t = 740/2.46666667 = 300
h = 0+4t/6 = 0+4 · 300/6 = 200
a = 0+6h/5 = 0+6 · 200/5 = 240

a = 240
h = 200
t = 300

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