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Kang Su · Answer 1 · 2023-08-24T06:56:15+0000

Solution

Let the three consecutive even integers be h, (h+2) and (h+4)

The consecutive integers add up to 36, i.e

Solve to find h

$\begin{gathered} \text{Open the brackets} \\ h+(h+2)+(h+4)=36 \\ h+h+2+h+4=36 \\ \text{Collect like terms} \\ h+h+h+2+4=36 \\ 3h+6=36 \\ \text{Collect like terms} \\ 3h=36-6 \\ 3h=30 \\ \text{Divide both sides by 3} \\ (3h)/(3)=(30)/(3) \\ h=10 \end{gathered}$

The greatest of the integers is h + 4,

The value of the greatest integer is

$\begin{gathered} h+4 \\ \text{Where }h=10 \\ h+4=10+4=14 \end{gathered}$

Hence, the greatest of the integers is 14

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