Question 96827
a) let x=smallest integer


b) 2nd integer: {{{y=x+2}}}, 3rd integer: {{{z=x+4}}} (remember consecutive even integers increment by 2 each time)



c) Sum: 
{{{x+y+z=114}}}


{{{x+(x+2)+(x+4)=114}}} Plug in {{{y=x+2}}} and {{{z=x+4}}}



d)

{{{x+x+2+x+4=114}}} Remove the parenthesis



{{{3x+6=114}}} Combine like terms on the left side



{{{3x=114-6}}}Subtract 6 from both sides



{{{3x=108}}} Combine like terms on the right side



{{{x=(108)/(3)}}} Divide both sides by 3 to isolate x




{{{x=36}}} Divide


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Answer:

So first number is {{{x=36}}} 




Now plug in {{{x=36}}} into the 2nd and 3rd number equations



2nd number: {{{36+2=38}}}
3rd integer: {{{36+4=40}}}



So the 3 numbers are


36, 38, 40




Check:


{{{36+38+40=114}}} Add up the 3 numbers. Their sum should equal 114


{{{114=114}}} works