Assume last year she had no money now. Then she spends 1/2 on clothes, and then 1/4 of the remaining money on toys  she had $7777 left.  How much money does she earn every month?

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Let A = monthly allowance, M = 12A (allowance total for one year)She starts with M, spends 1/2M on clothes and is left with:M - 1/2M = 1/2M = M/2Next, she spends 1/3 of her remaining money (M/2) on games, leaving her with:M/2 - (1/3)(M/2) = M/2 - M/6 = 2M/6 = M/3Next she spends 1/4 of her remaining money (M/3) on toys, leaving her with:M/3 - (1/4)(M/3) = M/3 - M/12 = 4M/12 - M/12 = 3M/12 = M/4This is her remaining money, M/4, which is 7777. So,M/4 = 7777M = 7777(4)M = 31,108But we want to know A:M = 12AA = M/12A = 31,108/12A = 2592.33, her monthly allowanceLet's check:(2592.33)(12) = 31108 Starting moneySpend 1/2 on clothes:31108 - (1/2)(31108) = 15554Spend 1/3 of this on games:15554 - (1/3)(15554) = 15554 - 5184.67 = 10369.33Spend 1/4 of this on toys:10369.33 - (1/4)(10369.33) = 10369.33 - 2492.33 = 7777 Checks!