19) Create a word problem to match the equation \( 40 \div x=2 \frac{1}{2} \). Define the variable \( x \). Find and interpret the solution.
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A local farmer has 40 apples that he wants to pack into boxes. Each box can hold the same number of apples, which we will call \( x \). If he ends up packing 2 and a half boxes, how many apples can fit into each box? To solve for \( x \), we can rewrite the equation \( 40 \div x = 2 \frac{1}{2} \), which is equivalent to \( 40 = 2.5x \). Then, dividing both sides by 2.5 gives \( x = \frac{40}{2.5} = 16 \). The solution tells us that each box can hold 16 apples. So, the farmer can neatly pack his apples into boxes of 16 without any leftovers!
