12. Higher Order Thinking Veronica needs to buy $$ 1 \frac{3}{4} $$ pounds of cheese. When the clerk places some cheese in a container and weighs it, the scale shows $$ 1 \frac{1}{4} $$ pounds. The container weighs $$ \frac{1}{16} $$ pound. How many more pounds of cheese should be added to the scale to get the amount that Veronica needs? Explain how you solved the problem.

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To determine how many more pounds of cheese Veronica needs to add to the scale to reach her desired amount of $$ 1 \frac{3}{4} $$ pounds, we'll follow these steps:

1. **Understand the Given Information:**
   - Veronica needs a total of $$ 1 \frac{3}{4} $$ pounds of cheese.
   - The current weight on the scale (cheese + container) is $$ 1 \frac{1}{4} $$ pounds.
   - The container itself weighs $$ \frac{1}{16} $$ pound.

2. **Calculate the Current Weight of Cheese on the Scale:**
   The scale shows the combined weight of the cheese and the container. To find just the weight of the cheese, subtract the weight of the container from the total weight on the scale.

$$
   \text{Weight of cheese} = \left(1 \frac{1}{4}\right) - \left(\frac{1}{16}\right)
   $$

First, convert $$ 1 \frac{1}{4} $$ to an improper fraction:

$$
   1 \frac{1}{4} = \frac{5}{4}
   $$

Now, subtract $$ \frac{1}{16} $$ from $$ \frac{5}{4} $$:

$$
   \frac{5}{4} - \frac{1}{16} = \frac{20}{16} - \frac{1}{16} = \frac{19}{16}
   $$

So, the current weight of the cheese on the scale is $$ \frac{19}{16} $$ pounds.

3. **Determine the Desired Total Weight of Cheese:**
   Veronica wants $$ 1 \frac{3}{4} $$ pounds of cheese. Let's convert that to an improper fraction:

$$
   1 \frac{3}{4} = \frac{7}{4} \text{ pounds}
   $$

4. **Calculate How Much More Cheese is Needed:**
   Subtract the current weight of the cheese from the desired weight to find out how much more cheese Veronica needs to add.

$$
   \frac{7}{4} - \frac{19}{16} = \frac{28}{16} - \frac{19}{16} = \frac{9}{16} \text{ pounds}
   $$

Therefore, Veronica needs to add $$ \frac{9}{16} $$ pounds of cheese to the scale to reach her desired total of $$ 1 \frac{3}{4} $$ pounds.

5. **Summary of Steps:**
   - **Convert mixed numbers to improper fractions** for easier calculation.
   - **Subtract the container's weight** to find the current cheese weight.
   - **Subtract the current cheese weight** from the desired total to find the additional amount needed.

By following these steps, you can determine that Veronica needs to add $$ \frac{9}{16} $$ pounds of cheese to achieve her goal.
Veronica needs to add $$ \frac{9}{16} $$ pounds of cheese to reach $$ 1 \frac{3}{4} $$ pounds total.

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