Explanation:
Here's a real-world problem involving a percent increase with decimals:
Suppose you have a savings account with a balance of $500. The bank offers an interest rate of 2.5% per year. How much will your balance increase after one year, including the interest earned?
To solve this problem, we can use the formula for percent increase:
Percent increase = (new value - old value) / old value x 100%
Let x be the amount of interest earned after one year. Then, the new value of the savings account after one year is:
New value = old value + interest earned
New value = $500 + x
The percent increase is given as 2.5%, which can be written as a decimal as 0.025. Using the formula above, we can write:
0.025 = (New value - $500) / $500 x 100%
Simplifying this equation, we get:
New value - $500 = $500 x 0.025
New value - $500 = $12.50
New value = $512.50
Therefore, the balance of the savings account will increase by $12.50 after one year, which represents a 2.5% increase from the original balance of $500. The new balance will be $512.50.