Calculating Percentage Increase in Unit Price of New Package vs Original Package
Let's tackle these questions step by step.
First, we need to determine what the price of the new package should be to keep the original package quantity to cost ratio the same.
The original package has 20 items for $5.75. So the cost per item is:
\( \frac{$5.75}{20 \text{ items}} = $0.2875 \text{ per item} \)
For the new package with 18 items to have the same cost ratio, the total package cost should be:
\( 18 \text{ items} \times $0.2875 \text{ per item} = $5.175 \)
However, since we are given that the price of the original and the new package is the same ($5.75), the calculation for a new package price that keeps the cost ratio the same is essentially a theoretical calculation to answer this part of the question.
Now, for the second part, the actual price of the new package is still $5.75, but it contains only 18 items. We need to calculate the new unit price and compare it with the original unit price to find the percentage increase.
New unit price with 18 items at $5.75 total cost is:
\( \frac{$5.75}{18 \text{ items}} = $0.3194 \text{ per item} \)
The percentage increase from the original unit price ($0.2875 per item) to the new unit price ($0.3194 per item) is:
\( \text{Percentage Increase} = \frac{\text{New Unit Price} - \text{Original Unit Price}}{\text{Original Unit Price}} \times 100 \% \)
\( \text{Percentage Increase} = \frac{$0.3194 - $0.2875}{$0.2875} \times 100 \% \)
\( \text{Percentage Increase} = \frac{$0.0319}{$0.2875} \times 100 \% \)
\( \text{Percentage Increase} = 0.111 \times 100 \% \)
\( \text{Percentage Increase} = 11.1 \% \)
So the unit price in the new package has increased by 11.1% compared to the original package. This is the final answer, rounded to one decimal place as requested.
