A man 24

A man distributed €25,300 among his 3 sons A, B, and C such that the amounts of their portions, with 10% simple interest over 2 years, 3 years, and 4 years respectively, will be equal. What is A's share?

Final Answer:

A =  9100 Eur

Step-by-step explanation:

t=25300 EUR r0​=10%=10010​=101​=0.1  S = A+2⋅ r0​⋅ A S = B+3⋅ r0​⋅ B S = C+4⋅ r0​⋅ C  A+2⋅ r0​⋅ A=B+3⋅ r0​⋅ B B+3⋅ r0​⋅ B=C+4⋅ r0​⋅ C A+B+C=t A+2⋅ 0.1⋅ A=B+3⋅ 0.1⋅ B B+3⋅ 0.1⋅ B=C+4⋅ 0.1⋅ C A+B+C=25300  1.2A−1.3B=0 1.3B−1.4C=0 A+B+C=25300  Row3−1.21​⋅ Row1→Row3 2.083B+C=25300  Pivot:Row2↔Row3  Row3−2.083333331.3​⋅ Row2→Row3 −2.024C=−15787.2  C=−2.024−15787.2​=7800 B=2.0833333325300−C​=2.0833333325300−7800​=8400 A=1.20+1.3B​=1.20+1.3⋅ 8400​=9100=9100 Eur  A=9100 B=8400 C=7800

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