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

Question

Ethan Adkins · Accepted Answer

Answer: #58,60,62#

Find the numbers when three consecutive even integers add up to 180.

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#.

Nathan Axel · Answer

#58,60,62# let the middle even numbe rbe #2n# Then, the others will be #2n-2" and "2n+2# #:. 2n-2+2n+2n+2=180# #=>6n=180# #n=30# The figures are #2n-2=2xx30-2=58# #2n=2xx30=60# #2n+2=2xx30+2=62#

Eli Assouline · Answer

see a solution process below;

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# Consequently, #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# Therefore, the following three numbers are; #x + 2 = 56 + 2 = 58# #x + 4 = 56 + 4 = 60# #x + 6 = 56 + 6 = 62#

Nathan Axel · Answer

undefined Let the three consecutive even integers be $x$, $x+2$, and $x+4$. The sum is given by the equation $x + (x+2) + (x+4) = 180$. Solve for $x$, then determine the three integers by adding 2 and 4 to the found value of $x$.