Siblings 48821

Three siblings saved CZK 1,445. Adela saved 10% less than Martin and David 10% more than Adela. How many crowns did each of them save?

Correct answer:

D =  495 Kc
A =  450 Kc
M =  500 Kc

Step-by-step explanation:

a=100%−10%=1−10010​=0.9 d=100%+10%=1+10010​=1.1  A+M+D=1445 A=a⋅ M D=d⋅ A A+M+D=1445 A=0.9⋅ M D=1.1⋅ A  A+D+M=1445 A−0.9M=0 1.1A−D=0  Pivot:Row1↔Row3 1.1A−D=0 A−0.9M=0 A+D+M=1445  Row2−1.11​⋅ Row1→Row2 1.1A−D=0 0.909D−0.9M=0 A+D+M=1445  Row3−1.11​⋅ Row1→Row3 1.1A−D=0 0.909D−0.9M=0 1.909D+M=1445  Pivot:Row2↔Row3 1.1A−D=0 1.909D+M=1445 0.909D−0.9M=0  Row3−1.909090910.90909091​⋅ Row2→Row3 1.1A−D=0 1.909D+M=1445 −1.376M=−688.095  M=−1.37619048−688.0952381​=500 D=1.909090911445−M​=1.909090911445−500​=495 A=1.10+D​=1.10+495​=450  A=450 D=495 M=500

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