Chapter 8, Problem 21CR

To determine

The solution of the equation $0.3\left(5+y\right)=12$ ,

Answer to Problem 21CR

  $y=35$

Explanation of Solution

Given:

The equation, $0.3\left(5+y\right)=12$

Concept Used:

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

• 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 $0.3\left(5+y\right)=12$ for the variable, isolate the variable term y on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate y on left side, first use Left distributive property and then subtract both sides by $1.5$ and then divide both sides by $0.3$ and then simplify further as shown below,

  $\begin{array}{c}0.3\left(5+y\right)=12\\ 0.3\cdot 5+0.3\cdot y=12\\ 1.5+0.3y=12\\ 1.5+0.3y-1.5=12-1.5\\ 0.3y=10.5\\ \frac{0.3y}{0.3}=\frac{10.5}{0.3}\\ y=35\end{array}$

Thus, the solution of the given equation is $y=35$ .