Applications of Linear Equations
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 \(84\) |