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At the Snack Shack


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When Jack went back for a late-night snack, he bought three items off the rack. Zack rang up the snacks and said "5.70, Jack." "Wait, Zack, you multiplied the prices instead of adding!" "Multiply, add; it still comes out the same. Pay up." What were the prices of Jack's three items?
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...on how the cash register deals with rounding...if it follows the "standard" round-half-up method, then I see 39 solutions:



1.06, 2.23, 2.41
1.06, 2.24, 2.40
1.06, 2.25, 2.39
1.06, 2.26, 2.38
1.06, 2.27, 2.37
1.06, 2.28, 2.36
1.06, 2.29, 2.35
1.06, 2.30, 2.34
1.07, 2.13, 2.50
1.07, 2.14, 2.49
1.08, 2.06, 2.56
1.08, 2.07, 2.55
1.09, 2.01, 2.60
1.09, 2.02, 2.59
1.10, 1.97, 2.63
1.11, 1.93, 2.66
1.12, 1.90, 2.68
1.13, 1.86, 2.71
1.14, 1.83, 2.73
1.15, 1.81, 2.74
1.16, 1.78, 2.76
1.17, 1.76, 2.77
1.18, 1.73, 2.79
1.19, 1.71, 2.80
1.20, 1.69, 2.81
1.21, 1.67, 2.82
1.22, 1.65, 2.83
1.24, 1.62, 2.84
1.25, 1.60, 2.85
1.27, 1.57, 2.86
1.29, 1.54, 2.87
1.31, 1.51, 2.88
1.32, 1.50, 2.88
1.35, 1.46, 2.89
1.36, 1.45, 2.89
1.37, 1.44, 2.89
1.38, 1.43, 2.89
1.39, 1.42, 2.89
1.40, 1.41, 2.89
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