Chapter 5.7, Problem 17E

To determine

To calculate : the value of $p$ in the given equation.

Answer to Problem 17E

The value of $p$ is $\frac{33}{17}$ .

Explanation of Solution

Given information :

Consider the equation provided in the question:

  $\frac{-41}{60}+\frac{17}{20}p=\frac{29}{30}$

Calculation :

As per the given problem

  $\frac{-41}{60}+\frac{17}{20}p=\frac{29}{30}$

Multiplying each side by the LCD of fractions,

The LCD of $60$ , $20$ and $30$ is $60$ .

  $60\times (\frac{-41}{60}+\frac{17}{20}p)=60\times (\frac{29}{30})$

Using distributive property,

  $60(\frac{-41}{60})+60(\frac{17}{20}p)=60(\frac{29}{30})$

Simplifying,

  $-41+51p=58$

Add $41$ to each side,

  $-41+51p+41=58+41$

Simplifying,

  $51p=99$

Dividing each side by $51$ ,

  $\frac{51}{51}p=\frac{99}{51}$

Simplifying,

  $p=\frac{99}{51}$ .

As $99$ and $51$ both are multiples of $3$ ,further simplifying,

  $p=\frac{33}{17}$

Hence,

The value of $p$ is $\frac{33}{17}$ .