Alright, let's determine the original amount given that 11.5% of it equals 782. Here's the step-by-step solution:
1. Understand the problem: We know that 11.5% of some original amount equals 782. We need to find what the original amount is.
2. Convert the percentage to a decimal:
Percent means per hundred, so:
[tex]\[
11.5\% = \frac{11.5}{100} = 0.115
\][/tex]
3. Set up the equation:
The equation for finding a part of a whole with percentage is:
[tex]\[
\text{part} = \text{percentage (as a decimal)} \times \text{original amount}
\][/tex]
Given:
[tex]\[
\text{part} = 782
\][/tex]
[tex]\[
\text{percentage (as a decimal)} = 0.115
\][/tex]
Let the original amount be [tex]\( x \)[/tex].
4. Formulate the equation with the given values:
[tex]\[
782 = 0.115 \times x
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], divide both sides of the equation by 0.115:
[tex]\[
x = \frac{782}{0.115}
\][/tex]
6. Calculate the division:
[tex]\[
x = 6800
\][/tex]
7. Conclusion:
The original amount is [tex]\( 6800 \)[/tex].
So, the original amount is 6800.
