A bottle of liquid laundry detergent priced at $\$ 16.50$ for a 42 -load bottle has been changed to $\$ 15.75$ for a 44 -load bottle. By what percentage has the price per load changed?
Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. For example $34.56 \%$
Answer
After calculating, we find that the price per load has changed by \(\boxed{-2.38\%}\).
Step 1 ：First, we need to calculate the price per load for both the old and new bottle. For the old bottle, the price per load is \(\frac{16.50}{42}\) dollars per load, and for the new bottle, the price per load is \(\frac{15.75}{44}\) dollars per load.
Step 2 ：Next, we calculate the change in price per load by subtracting the price per load of the new bottle from the price per load of the old bottle. This gives us \(\frac{16.50}{42} - \frac{15.75}{44}\) dollars per load.
Step 3 ：Then, we divide this change by the original price per load (the price per load of the old bottle) to find the proportion of the change. This gives us \(\frac{\frac{16.50}{42} - \frac{15.75}{44}}{\frac{16.50}{42}}\).
Step 4 ：Finally, we multiply this proportion by 100 to convert it to a percentage. This gives us \(\frac{\frac{16.50}{42} - \frac{15.75}{44}}{\frac{16.50}{42}} \times 100\) percent.
Step 5 ：After calculating, we find that the price per load has changed by \(\boxed{-2.38\%}\).
