After a 20% increase, the new price of a radio is $78.00. What was the original price of the radio?

Options

A. `$15.60`
B. `$60.00`
C. `$62.40`
D. `$65.00`

Answer

To find the original price of the radio before the 20% increase, we can follow these steps:

1. **Understand the Problem**: We know that after a 20% increase, the new price of the radio is $78. We need to find the original price (let's call it \( x \)).

2. **Set Up the Equation**: A 20% increase means that the new price is 120% of the original price. We can express this mathematically as:
\[ 120\% \text{ of } x = 78 \]
In decimal form, 120% can be written as \( \frac{120}{100} \) or \( 1.2 \). Therefore, we can rewrite the equation as:
\[ 1.2x = 78 \]

3. **Solve for \( x \)**: To find \( x \), we need to isolate it. We can do this by dividing both sides of the equation by 1.2:
\[ x = \frac{78}{1.2} \]

4. **Calculate \( x \)**: Now, we perform the division:
\[ x = \frac{78}{1.2} = 65 \]

5. **Conclusion**: The original price of the radio was $65.

Thus, the original price of the radio is **$65**.