Three friends

Peter is eight times older than Rado, and Rado is three times younger than Joseph. Together they have 120 years. Determine how many are each of them.

Correct answer:

P =  80
R =  10
J =  30

Step-by-step explanation:


P=8·R
R = J/3
P+R+J= 120

P-8R = 0
J-3R = 0
J+P+R = 120

Pivot: Row 1 ↔ Row 2
J-3R = 0
P-8R = 0
J+P+R = 120

Row 3 - Row 1 → Row 3
J-3R = 0
P-8R = 0
P+4R = 120

Row 3 - Row 2 → Row 3
J-3R = 0
P-8R = 0
12R = 120


R = 120/12 = 10
P = 0+8R = 0+8 · 10 = 80
J = 0+3R = 0+3 · 10 = 30

J = 30
P = 80
R = 10

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algebrabasic operations and conceptsUnits of physical quantitiesGrade of the word problem

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