The sum of three consecutive even #s is 144; what are the numbers?

2 Answers
May 30, 2016

Answer:

They are 46, 48, 50.

Explanation:

An even number is a multiple of #2#, then can be written as 2n. The next even number after #2n# is #2n+2# and the following is #2n+4.#
So you are asking for which value of #n# it you have

#(2n)+(2n+2)+(2n+4)=144#

I solve it for #n#

#6n+6=144#
#n=138/6=23#.

The three numbers are

#2n=2*23=46#
#2n+2=46+2=48#
#2n+4=46+4=50#

May 30, 2016

Answer:

The numbers are 46, 48 and 50.

Explanation:

First define the consecutive even numbers:

Even numbers, such as 8, 10, 12 etc. differ by 2.

We could call the numbers #x, x+2 and x+4#, but there is no guarantee that x is even.

However, an even number can be divided by 2, so any number given as #2x# is definitely even.

SO, let the consecutive even numbers be #2x, 2x + 2 and 2x + 4#
Their sum is 144, so write an equation:

#2x + (2x + 2) + (2x + 4) = 144#

#6x + 6 = 144#
#6x = 138#
#x = 23#

However, we defined the first even number as #2x#.

#2 xx 23 = 46#

The numbers are 46, 48 and 50.