If the sum of 3 consecutive even integers is 30 how do you find the numbers?

2 Answers
Alan P.
Sep 6, 2015

The three numbers are 9, 10, and 11

Explanation:

Let #n# be the smallest of the three consecutive numbers
#rarr# the other two numbers are #n+1# and #n+2#

We are told
#color(white)("XXX")(n) + (n+1) + (n+2) = 30#

#rarr color(white)("XX")3n+ 3 = 30#

#rarr color(white)("XX")3n = 27#

#rarr color(white)("XX")n = 9#

Babette
Sep 6, 2015

#8#, #10# and #12#

Explanation:

We can define an even number as #2x#

Let #2x# be the first even number

Let #2x+2# be the next even number

Let #2x+4# be the last one

Their sum is #30# so we write

#2x+(2x+2)+(2x+4)=30#

Combining like terms

#6x+6=30#

#6x=24#

#x=4#

So

#2x=2(4)=8#

#2x+2=8+2=10#

#2x+4=8+4=12#

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