Applications of Linear Equations

This section this textbook explains how to translate the situations described in word problems to equations and provides a variety of examples. Read the chapter and work through the problems. Some examples involved the geometric facts you have learned in Unit 2.

Example 103.

Fifteen more than three times a number is the same as ten less than six times the number. What is the number?

$3x + 15$	First, addition is built backwards
$6x − 10$	Then, subtraction is also built backwards
$3x + 15 = 6x − 10$	Is between the parts tells us they must be equal
$\underline {− 3x − 3x}$	Subtract $3x$ so variable is all on one side
$15 = 3x − 10$	Now we have a two − step equation
$\underline {+10 \quad+10}$	Add $10$ to both sides
$\underline {25 =3x}$	The variable is multiplied by $3$
$3 \quad \quad 3$	Divide both sides by $3$
$\frac {25}{3} = x$	Our number is $\frac {25}{3}$

Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other, such as 3, 4, 5. If we are looking for several consecutive numbers it is important to first identify what they look like with variables before we set up the equation. This is shown in the following example.