Proportions: 2742

The three siblings' ages are in such proportions: E: J = 5:4, J: P = 3:2. They are a total of 35 years old. How old are Eva, Jožo, and Peter?

Correct answer:

E =  
J =  12
P =  8

Step-by-step explanation:


E+J+P=35
4E=5J
2J=3P

e+J+P=35
4·e=5·J
2·J=3·P

J+P+e = 35
5J-4e = 0
2J-3P = 0

Pivot: Row 1 ↔ Row 2
5J-4e = 0
J+P+e = 35
2J-3P = 0

Row 2 - 1/5 · Row 1 → Row 2
5J-4e = 0
P+1.8e = 35
2J-3P = 0

Row 3 - 2/5 · Row 1 → Row 3
5J-4e = 0
P+1.8e = 35
-3P+1.6e = 0

Pivot: Row 2 ↔ Row 3
5J-4e = 0
-3P+1.6e = 0
P+1.8e = 35

Row 3 - 1/-3 · Row 2 → Row 3
5J-4e = 0
-3P+1.6e = 0
2.333e = 35


e = 35/2.33333333 = 15
P = 0-1.6e/-3 = 0-1.6 · 15/-3 = 8
J = 0+4e/5 = 0+4 · 15/5 = 12

J = 12
P = 8
e = 15

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