Unknown amount of money

Damian and Denis split an unknown amount in the ratio of 5:4. Damian got six euros more than Denis. Calculate an unknown amount. Determine how much money Damian got and how much Denis got.

Correct answer:

a =  30
b =  24
x =  54

Step-by-step explanation:


4a=5b
a=6+b
x=a+b

4·a=5·b
a=6+b
x=a+b

4a-5b = 0
a-b = 6
a+b-x = 0

Row 2 - 1/4 · Row 1 → Row 2
4a-5b = 0
0.25b = 6
a+b-x = 0

Row 3 - 1/4 · Row 1 → Row 3
4a-5b = 0
0.25b = 6
2.25b-x = 0

Pivot: Row 2 ↔ Row 3
4a-5b = 0
2.25b-x = 0
0.25b = 6

Row 3 - 0.25/2.25 · Row 2 → Row 3
4a-5b = 0
2.25b-x = 0
0.111x = 6


x = 6/0.11111111 = 54
b = 0+x/2.25 = 0+54/2.25 = 24
a = 0+5b/4 = 0+5 · 24/4 = 30

a = 30
b = 24
x = 54

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You need to know the following knowledge to solve this word math problem:

algebrabasic operations and conceptsUnits of physical quantitiesGrade of the word problem

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