To determine the least number of bags needed to hold 51 pounds of sugar, we can use a method called linear Diophantine equations. We need to find integers x and y that satisfy the equation 4x + 5y = 51, where x represents the number of 4-pound bags and y represents the number of 5-pound bags. By solving this equation, we find that the least number of bags required is 9, with 3 bags weighing 4 pounds each and 6 bags weighing 5 pounds each.
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