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.