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 $(80)+ 2= 82$ Third $(80)+ 4= 84$	The numbers are $80$ , $82$ , and $84$