Solution
Let the three consecutive even integers be h, (h+2) and (h+4)
The consecutive integers add up to 36, i.e
[tex]h+(h+2)+(h+4)=36[/tex]
Solve to find h
[tex]\begin{gathered} \text{Open the brackets} \\ h+(h+2)+(h+4)=36 \\ h+h+2+h+4=36 \\ \text{Collect like terms} \\ h+h+h+2+4=36 \\ 3h+6=36 \\ \text{Collect like terms} \\ 3h=36-6 \\ 3h=30 \\ \text{Divide both sides by 3} \\ \frac{3h}{3}=\frac{30}{3} \\ h=10 \end{gathered}[/tex]
The greatest of the integers is h + 4,
The value of the greatest integer is
[tex]\begin{gathered} h+4 \\ \text{Where }h=10 \\ h+4=10+4=14 \end{gathered}[/tex]
Hence, the greatest of the integers is 14
