Find the percent of increase from 68 songs to 75 songs. Round to the nearest tenth of a percent if necessary.
The Correct Answer and Explanation is:
To find the percent increase from 68 songs to 75 songs, we can use the formula for percent increase:
[
\text{Percent Increase} = \left( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \right) \times 100
]
In this case:
- Old Value = 68 songs
- New Value = 75 songs
First, we calculate the increase in the number of songs:
[
\text{Increase} = \text{New Value} – \text{Old Value} = 75 – 68 = 7
]
Next, we plug the values into the percent increase formula:
[
\text{Percent Increase} = \left( \frac{7}{68} \right) \times 100
]
Now, we calculate ( \frac{7}{68} ):
[
\frac{7}{68} \approx 0.10294117647
]
Now we multiply by 100 to convert it to a percentage:
[
0.10294117647 \times 100 \approx 10.294117647
]
Finally, rounding to the nearest tenth of a percent:
[
10.294117647 \approx 10.3\%
]
Thus, the percent increase from 68 songs to 75 songs is approximately 10.3%.
Explanation
The concept of percent increase is widely used to measure growth or change in various contexts, such as finance, population studies, and other quantitative fields. In this scenario, we are analyzing the change in the number of songs from 68 to 75. To effectively gauge this change, we need to establish the initial (old) value and the final (new) value.
The difference between the two values provides us with the increase, which quantifies how much growth has occurred. By dividing the increase by the original number of songs (68), we derive a ratio that indicates how significant the increase is relative to the original quantity. This ratio is then converted to a percentage by multiplying by 100, which allows for a more intuitive understanding of the increase.
Percentages provide a standardized way to compare changes across different contexts, making it easier to communicate and interpret growth. In this case, the increase from 68 songs to 75 songs, expressed as approximately 10.3%, indicates a meaningful growth in the collection of songs, highlighting an enhancement in the number of items available for listening.