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Find three consecutive even integers which sum is 138.​

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[tex] \large\underline \bold{{SOLUTION}}[/tex]

[tex]\textsf{\small{The three consecutive integers can be}}[/tex][tex]\textsf{\small{illustrated as:}}[/tex]

[tex]\textrm{First even integer = x}[/tex][tex]\textrm{Second even integer = x+2}[/tex][tex]\textrm{Third even integer = x+4}[/tex]

[tex]\textsf{\underline{We will equate the sum to 138}}[/tex]

[tex]\longmapsto\rm{1st+2nd+3rd=138}[/tex]

[tex]\longmapsto\rm{(x)+(x+2)+(x+4)=138}[/tex]

[tex]\longmapsto\rm{3x+6=138}[/tex]

[tex]\longmapsto\rm{3x=138-6}[/tex]

[tex]\longmapsto\rm{3x=132}[/tex]

[tex]\longmapsto\underline{\rm{x=44}}[/tex]

[tex]\textsf{\underline{Now, We will substitute the value of x}}[/tex][tex]\textsf{\underline{to get the value of the integers.}}[/tex]

[tex]\textrm{First even integer = x = \boxed{44}}[/tex]

[tex]\textrm{Second even integer = x+2 = 44+2 = \boxed{46}}[/tex]

[tex]\textrm{Third even integer = x+4 = 44+4 = \boxed{48}}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • The three even integers are 44 , 46 , and 48
MissJindySummerviz

CONSECUTIVE INTEGERS

Find 3 consecutive even integers which sum is 138.​

[tex]{\underline{\bold{Representations:}}}[/tex]

[tex]\textsf{\small{Let x be the first even integer}}\\\textsf{\small{Then x + 2 be the second even integer}}\\\textsf{\small{And x + 4 be the third even integer}}\\\textsf{\small{Their sum is 138}}[/tex]

[tex]{\underline{\bold{Solution:}}}[/tex]

[tex]\tt{x+x+2+x+4=138}\\\tt{3x+6=138}\\\tt{3x=138-6}\\\tt{3x=132}\\\tt{x=132\div3}\\\tt{x=44}[/tex]

[tex]\tt{x+2}\\\tt{44+2=46}[/tex]

[tex]\tt{x+4}\\\tt{44+4=48}[/tex]

The first even integer is 44, the second even integer is x + 2 or 46, and the third even integer is x + 4 or 48.

[tex]{\underline{\bold{Checking:}}}[/tex]

[tex]\tt{44+46+48=138}\\\tt{90+48=138}\\\tt{138=138}[/tex]

[tex]{\underline{\mathcal{REMEMBER:}}}[/tex]

  • Consecutive even integers are even numbers in an uninterrupted order which is the same as when you count by twos such as 2, 4, 6, 8, and 10.
  • Note that consecutive even and odd integers are represented in the same way, but the variable x represents a different kind of number in the two cases.

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