What is the solution of 82.78(p+11.892)=72.8464

Question

82.78
(
𝑝
+
11.892
)
=
72.8464
when solving for p
𝑝
? Do not round your answer.(1 point)

Answer 1

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

1. Divide both sides by 82.78 to isolate the term with \( p \): \[ p + 11.892 = \frac{72.8464}{82.78} \] Calculating the right side: \[ p + 11.892 = 0.8797 \quad (approximately) \]

2. Subtract 11.892 from both sides: \[ p = 0.8797 - 11.892 \] So, \[ p = -11.0123 \quad (approximately) \]

Thus, the exact value for \( p \) without rounding is:

\[ p = \frac{72.8464}{82.78} - 11.892 \]

Calculating it more precisely:

First, compute \( \frac{72.8464}{82.78} \): \[ \frac{72.8464}{82.78} = 0.879699 \]

Then: \[ p = 0.879699 - 11.892 \] \[ p = -11.012301 \quad (exact) \]

So the solution for \( p \) is: \[ p = -11.012301 \]