Two men

Two men earn in the ratio 5 : 3 and expend in the ratio 9: 5. If each saves 30000 USD every year, find their income.

Correct answer:

a =  300000 USD
b =  180000 USD

Step-by-step explanation:

a:b=5:3 A:B=9:5  3a=5b 5A = 9B  a−A = 30000 b−B = 30000  a−A=30000 3/5a−5/9A=30000  a−A=30000 3/5⋅ a−5/9⋅ A=30000  A−a=−30000 25A−27a=−1350000  Pivot:Row1↔Row2 25A−27a=−1350000 A−a=−30000  Row2−251​⋅ Row1→Row2 25A−27a=−1350000 0.08a=24000  a=0.0824000​=300000 A=25−1350000+27a​=25−1350000+27⋅ 300000​=270000  A=270000 a=300000=300000 USD
b=53​⋅ a=53​⋅ 300000=53⋅ 300000​=5900000​=180000 USD

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