Find the percent of increase from 25 basketballs to 35 basketballs.
The Correct Answer and Explanation is :
To find the percent increase from 25 basketballs to 35 basketballs, we use the formula:
[
\text{Percent Increase} = \left(\frac{\text{New Value} – \text{Old Value}}{\text{Old Value}}\right) \times 100
]
In this case:
- New Value = 35 basketballs
- Old Value = 25 basketballs
Substitute the values into the formula:
[
\text{Percent Increase} = \left(\frac{35 – 25}{25}\right) \times 100 = \left(\frac{10}{25}\right) \times 100 = 0.4 \times 100 = 40\%
]
Explanation:
The problem involves determining how much of a change has occurred between two quantities — from 25 basketballs to 35 basketballs. Percent increase is a way to express this change as a portion of the original value, giving us a sense of how large the increase is relative to where we started.
Step-by-Step Process:
- Find the difference between the new value and the old value. This difference represents how many more basketballs there are now compared to the original amount. In this case, the difference is:
[
35 – 25 = 10 \text{ basketballs}.
] - Divide the difference by the original value to see what fraction or portion of the original number this increase represents. Here, we take 10 (the difference) and divide it by 25 (the original amount of basketballs):
[
\frac{10}{25} = 0.4.
]
This shows that the increase is 40% of the original amount. - Convert the decimal to a percentage by multiplying by 100:
[
0.4 \times 100 = 40\%.
]
So, the percent increase from 25 basketballs to 35 basketballs is 40%.
Percent increase is useful because it provides a way to understand how significant a change is, no matter the original size. In this example, the 40% increase tells us the new number of basketballs is 40% greater than the starting point of 25.