Determine 3805

Denis has 43% more money than Damian, and Zuzana has 12% less money than Damian. They have a total of 165 euros and 50 cents. Determine how much money Denis, Damian, and Zuzana have.

Correct answer:

a =  71.5
b =  50
c =  44

Step-by-step explanation:


a=1.43 b
c = (1-0.12)b
a+b+c=165.50

a=1.43·b
c = (1-0.12)·b
a+b+c=165.50

a-1.43b = 0
0.88b-c = 0
a+b+c = 165.5

Row 3 - Row 1 → Row 3
a-1.43b = 0
0.88b-c = 0
2.43b+c = 165.5

Pivot: Row 2 ↔ Row 3
a-1.43b = 0
2.43b+c = 165.5
0.88b-c = 0

Row 3 - 0.88/2.43 · Row 2 → Row 3
a-1.43b = 0
2.43b+c = 165.5
-1.362c = -59.934


c = -59.93415638/-1.36213992 = 44
b = 165.5-c/2.43 = 165.5-44/2.43 = 50
a = 0+1.43b = 0+1.43 · 50 = 71.5

a = 143/2 = 71.5
b = 50
c = 44

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