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This question is easier to use algebra to find the factors for each type with a difference of 54.
Let d be the factor for donuts and m be the factor for muffins.
7d – 3m = 54 (donuts bought was 54 more than muffins)
6m = 10d (same amount was spent on both since she spent 1/2 her money on donuts =>
half was on muffins)
m = (10/6)d = (5/3)d
7d – 3(5/3)d = 54
2d=54 => d = 27
m = (5/3) x 27 = 5 x 9 = 45
Hence total amount of money Amy has at first is 6m +10d = 270 + 270 = $540