The sum of three consecutive even integers is 180. How do you find the numbers?

3 Answers
Mar 21, 2018

Answer: #58,60,62#

Explanation:

Sum of 3 consecutive even integers is 180; find the numbers.

We can start by letting the middle term be #2n# (note that we can't simply use #n# since it would not guarantee even parity)

Since our middle term is #2n#, our other two terms are #2n-2# and #2n+2#. We can now write an equation for this problem!
#(2n-2)+(2n)+(2n+2)=180#

Simplifying, we have:
#6n=180#

So, #n=30#

But we're not done yet. Since our terms are #2n-2,2n,2n+2#, we must substitute back in to find their values:
#2n=2*30=60#
#2n-2=60-2=58#
#2n+2=60+2=62#

Therefore, the three consecutive even integers are #58,60,62#.

Mar 21, 2018

#58,60,62#

Explanation:

let the middle even numbe rbe #2n#

the others will then be

#2n-2" and "2n+2#

#:. 2n-2+2n+2n+2=180#

#=>6n=180#

#n=30#

the numbers are

#2n-2=2xx30-2=58#

#2n=2xx30=60#

#2n+2=2xx30+2=62#

Mar 21, 2018

see a solution process below;

Explanation:

Let the three consecutive even integers be represented as; #x+2 , x+4, and x+6#

Hence the sum of three consecutive even integers should be; #x+2 + x+4 + x+6 = 180#

Therefore;

#x+2 + x+4 + x+6 = 180#

#3x + 12 = 180#

Subtract #12# from both sides;

#3x + 12 - 12 = 180 - 12#

#3x = 168#

Divide both sides by #3#

#(3x)/3 = 168/3#

#(cancel3x)/cancel3 = 168/3#

#x = 56#

Hence the three consecutive numbers are;

#x + 2 = 56 + 2 = 58#

#x + 4 = 56 + 4 = 60#

#x + 6 = 56 + 6 = 62#