Question #1ea10

3 Answers
Oct 15, 2017

#68,70,72#

Explanation:

I'm not sure what you mean by "find two numbers". I'll just show you how to get all three and hopefully you can get your answer from that.

Let's let #x# be the middle of the three even integers. Then the even integer less than #x# has to be #x-2# and the one above has to be #x+2# because the even integers are consecutive.

We know that the sum is #210#. Thus:

#(x)+(x-2)+(x+2)=210#

#3x=210#

#x=70#

Thus, our middle even integer is #70#. The other even integers are #70-2=68# and #70+2=72#.

As we can see, #68,70,72# are consecutive even integers and #68+70+72=210#.

Oct 15, 2017

Any two numbers from the set #{68,70,72}#

Explanation:

Any number is even when it is doubled, so #e=2n, ninZZ#

So, a set of even numbers will be #E={2n,2n+2,2n+4,\cdots}#

Three consecutive numbers that add up to 210 will follow the formula:
#210=2n+2n+2+2n+4=6n+6#

#6(n+1)=210#

#n+1=210/6=35#

#n=35-1=34#

The three consecutive numbers that add up to 210 are #{2(34),2(34)+2,2(24)+4}={68,70,72}#

Oct 15, 2017

#68, 70, 72#

Explanation:

Let the consecutive numbers be #x, x+2, x+4#

#x + (x+2) + (x+4) = 210 -> "Statement"#

Solving..

#x + x + 2 + x + 4 = 210#

#3x + 6 = 210#

#3x = 210 - 4#

#3x = 204#

#x = 204/3#

#x = 68#

Hence

The numbers are

#x = 68#,

#x + 2 = 70#

#x + 4 = 72#