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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**Word Problem:**  
A baker has 40 identical cupcakes and wants to package them into boxes so that each box contains the same number of cupcakes. If after filling the boxes each box has exactly $$2\frac{1}{2}$$ cupcakes, how many boxes, $$x$$, did the baker use?

**Definition of the Variable:**  
Let $$ x $$ be the number of boxes used to package the 40 cupcakes.

**Step-by-Step Solution:**

1. **Set Up the Equation:**  
   The equation according to the problem is  
   $$
   \frac{40}{x} = 2\frac{1}{2}
   $$
   
2. **Convert the Mixed Number to an Improper Fraction:**  
   The mixed number $$2\frac{1}{2}$$ can be expressed as an improper fraction:  
   $$
   2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
   $$
   So, the equation becomes  
   $$
   \frac{40}{x} = \frac{5}{2}
   $$

3. **Solve for $$ x $$:**  
   Cross-multiply to eliminate the fractions:
   $$
   40 \times 2 = 5 \times x
   $$
   Simplify:
   $$
   80 = 5x
   $$
   Divide both sides by 5:
   $$
   x = \frac{80}{5} = 16
   $$

4. **Interpret the Solution:**  
   The value $$ x = 16 $$ means that the baker used 16 boxes to package the 40 cupcakes, with each box containing $$2\frac{1}{2}$$ cupcakes.

**Word Problem:** A baker has 40 identical cupcakes and wants to package them into boxes so that each box contains the same number of cupcakes. If after filling the boxes each box has exactly $$2\frac{1}{2}$$ cupcakes, how many boxes, $$x$$, did the baker use? **Solution:** The baker used 16 boxes to package the 40 cupcakes, with each box containing $$2\frac{1}{2}$$ cupcakes.

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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