Applications of Linear Equations
Completion requirements
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 105.
The sum of three consecutive even integers is \(246\). What are the numbers?
| First \(x\) | Make the first \(x\) |
| Second \(x +2\) | Even numbers, so we add \(2\) to get the next |
| Third \(x +4\) | Add \(2\) more (\(4\) total)to get the third |
| \(F + S + T = 246\) | Sum means add First \((F)\) plus Second \((S)\) plus Third \((T)\) |
| \((x)+ (x +2) +(x + 4)= 246\) | Replace each \(F\), \(S\), and \(T\) with what we labeled them |
| \(x + x +2 + x + 4= 246\) | Here the parenthesis are not needed |
| \(3x + 6= 246\) | Combine like terms \(x + x + x\) and \(2+ 4\) |
| \(\underline {− 6 \quad − 6}\) | Subtract \(6\) from both sides |
| \( \underline {3x = 240}\) | The variable is multiplied by \(3\) |
| \(3 \quad \quad 3\) | Divide both sides by \(3\) |
| \(x = 80\) | Our solution for \(x\) |
| First \(80\) | Replace \(x\) in the original list with \(80\). |
|
Second \((80)+ 2= 82\) |
The numbers are \(80\), \(82\), and \(84\) |