Question

four tears ago marins was three times old as her daughter.six years from now the mother will be twice as old as her daughter. find their present ages​

Answer 1

Correct question

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Four years ago Marina was three times old as her daughter. Six years from now the mother will be twice as old as her daughter. Find their present ages

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A n s w e r

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G i v e n

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• Four years ago Marina was three times old as her daughter

• Six years from now the mother will be twice as old as her daughter

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F i n d

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• Their present ages

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S o l u t i o n

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Let the present age of Marina be "a"

Let the present age of her daughter be "b"

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$\underline{\bold{\texttt{Four years ago Marina's age :}}}$

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➠ a - 4

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$\underline{\bold{\texttt{Four years ago her daughter's age :}}}$

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➠ b - 4

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Given that, four years ago Marina was three times old as her daughter

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➜ (a - 4) = 3(b - 4)

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➜ a - 4 = 3b - 12

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➜ a - 3b = - 12 + 4

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➜ a - 3b = -8 ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{6 years later Marina's age :}}}$

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➠ a + 6

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$\underline{\bold{\texttt{6 years later her daughter's age :}}}$

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➠ b + 6

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Given that , six years from now the mother will be twice as old as her daughter

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➜ (a + 6) = 2(b + 6)

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➜ a + 6 = 2b + 12

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➜ a - 2b = 12 - 6

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➜ a - 2b = 6 ⚊⚊⚊⚊ ⓶

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⟮ Equation ⓶ - ⓵ ⟯

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➜ a - 2b -(a - 3b) = 6 - (-8)

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➜ a - 2b - a + 3b = 6 + 8

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➨ b = 14 ⚊⚊⚊⚊ ⓷

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• Hence her daughter's present age is 14 years

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⟮ Putting b = 14 from ⓷ to ⓵ ⟯

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➜ a - 3b = -8

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➜ a - 3(14) = -8

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➜ a - 42 = -8

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➜ a = -8 + 42

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➨ a = 34

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• Hence Marina is 34 years old

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∴ The present ages of mother and her daughter are 34 years & 14 years respectively