Chapter 8.2, Problem 17CYU

To determine

the solution of the proportion $\frac{5p-1}{11}=\frac{3-5p}{6}$ .

Answer to Problem 17CYU

  $C.\frac{39}{85}$

Explanation of Solution

Given:

The proportion, $\frac{5p-1}{11}=\frac{3-5p}{6}$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $\frac{5p-1}{11}=\frac{3-5p}{6}$ for the variable, isolate the variable term p on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate p on both side, first multiply both sides by 6 and then multiply both sides by 11 and then add both sides by 55p and then simplify the like terms and then add both sides by 6 and then simplify further divide both sides by 85 as shown below,

  $\begin{array}{c}\frac{5p-1}{11}=\frac{3-5p}{6}\\ \frac{5p-1}{11}\cdot 6=\frac{3-5p}{6}\cdot 6\\ \frac{30p-6}{11}=3-5p\\ \frac{30p-6}{11}\cdot 11=11\cdot \left(3-5p\right)\\ 30p-6=33-55p\\ 30p-6+55p=33-55p+55p\\ 85p-6=33\\ 85p-6+6=33+6\\ 85p=39\\ \frac{85p}{85}=\frac{39}{85}\\ p=\frac{39}{85}\end{array}$

Thus, the value of $p=\frac{39}{85}$ .