Question

What is the solution of 82.78(p+11.892)=72.8464
when solving for p
?

Answer 1

To solve the equation \( 82.78(p + 11.892) = 72.8464 \) for \( p \), follow these steps:

1. **Distribute the left side**:
\[
82.78p + 82.78 \times 11.892 = 72.8464
\]
First, calculate \( 82.78 \times 11.892 \):
\[
82.78 \times 11.892 \approx 986.024856
\]
So the equation becomes:
\[
82.78p + 986.024856 = 72.8464
\]

2. **Isolate the term with \( p \)**:
Subtract \( 986.024856 \) from both sides:
\[
82.78p = 72.8464 - 986.024856
\]

3. **Calculate the right side**:
\[
72.8464 - 986.024856 \approx -913.178456
\]
So now the equation is:
\[
82.78p = -913.178456
\]

4. **Solve for \( p \)**:
Divide both sides by \( 82.78 \):
\[
p = \frac{-913.178456}{82.78} \approx -11.0301
\]

Thus the solution for \( p \) is approximately:
\[
\boxed{-11.0301}
\]