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A farmer delivers 252 lb of apples to the local grocer, who divides them into 5 lb and 2 lb bags. How many bags did he have to sell?

a) 18 bags
b) 21 bags
c) 24 bags
d) 28 bags

User Ebonique
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1 Answer

4 votes

Final answer:

The question is a basic arithmetic problem that requires setting up an equation and solving for two variables representing the number of 5 lb and 2 lb bags. By systematically trying different combinations, we determine the grocer would have made a total of 54 bags to account for all 252 lbs of apples.

Step-by-step explanation:

The question involves a basic arithmetic and algebra problem where a farmer has to divide a total weight of apples into smaller bags of two specific weights. To find out how many bags the grocer made, we need to assign variables to the unknowns - let's say x is the number of 5 lb bags, and y is the number of 2 lb bags. Since the total weight of the apples is 252 pounds, we can write the following equation:



5x + 2y = 252



Now, we need to find values of x and y that satisfy this equation. One approach is to divide the total weight by the larger bag size, which gives us a starting point:



252 ÷ 5 = 50.4



Since we can't have a fraction of a bag, we consider the largest whole number less than or equal to 50.4, which is 50. This would mean:



5 * 50 = 250 pounds



That leaves 2 pounds of apples unaccounted for, which can't be right as we need to use up all 252 pounds. We could then try one less 5 lb bag, so 49 bags of 5 lb each:



5 * 49 = 245 pounds



Then we divide the remaining weight by 2 lb per bag:



(252 - 245) ÷ 2 = 3.5



Again, we can't have half a bag, so we need to adjust again. If we try 48 bags of 5 lb each:



5 * 48 = 240 pounds



And for 2 lb bags:



(252 - 240) ÷ 2 = 6 bags



Therefore, the grocer would have 48 + 6 = 54 bags in total.

User Pzmarzly
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