Question

Write and solve the equation for the sentence “One half of a number increased by 16 is four less than two thirds of the number.”

Short answer

The equation for the given problem is $\frac{1}{2}x+16=\frac{2}{3}x-4$.

The value of the number is 120.

Step-by-step solution

Step-1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Step-2. Concept of equation.

Equations: - Equations are the statements in which two expressions are equal. The expression can be created by variables, constants, numbers and symbols.

Step-3. Solution of the given problem.

The given problem is:

One-half of a number increased by 16 is four less than two-thirds of a number.

Let the number be x.

The given problem can be written in the form of an equation as

$\frac{1}{2}x+16=\frac{2}{3}x-4$

Add $-\frac{2}{3}x-16$to both sides of the equation.

$\begin{array}{l}\frac{1}{2}x+16-\frac{2}{3}x-16=\frac{2}{3}x-4-\frac{2}{3}x-16\\ \frac{1}{2}x-\frac{2}{3}x+16-16=\frac{2}{3}x-\frac{2}{3}x-4-16\\ \frac{3-4}{6}x=-20\\ -\frac{1}{6}x=-20\end{array}$

Multiply $-6$to both sides of the equation.

$\begin{array}{l}-6\times \frac{\left(-1\right)}{6}x=-6\times \left(-20\right)\\ x=120\end{array}$

Hence, the number is 120.