Right now, Alan's mother is 4 times older than he is. In 4 years, she will be 3 times older than he is. How how old are Alan and his mother right now?

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Solution

Let Alan's age beX
Alan's mother is 4 times older than he is.
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Mother's age = 4X
`
>>...In 4 years,...<<
`
` (Alan's age in 4 years) = X+4
(Mother's age in 4 years) = 4X+4
`
>>...In 4 years, she will be 3 times older than he is...<<
`
(Mother's age in 4 years) = 3 times (Allen's age in 4 years)
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` ` ` ` ` ` ` ` ` ` `4X+4 = 3(X+4)
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X = 8, ie Alan's age=8 &Mother's age = 4×8 = 32

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