# Ages Complicated

Algebra Level 4

When Jane is one year younger than Betty will be when Jane is half as old as Betty will be when Jane is twice as old as Betty is now, Betty will be three times as old as Jane was when Betty was as old as Jane is now. One is in her teens and ages are in completed years. $$\alpha$$ Denotes Age From Jane and $$\beta$$ Denotes Age From Betty

Find $$\alpha + \beta$$

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