Four consecutive integers are such that the sum of the #2#nd and #4#th integers is #132#. What are the four integers?

2 Answers
Sep 13, 2016

#64, 65, 66, 67#

Explanation:

Suppose the integers are:

#n-2, n-1, n, n+1#

Then we are given:

#132 = (n-1) + (n+1) = 2n#

Dividing both ends by #2# and transposing, we find:

#n = 66#

So the four integers are:

#64, 65, 66, 67#

Sep 13, 2016

The four consecutive integers are 64,65, 66 and 67.

Explanation:

Consecutive integers are found by adding 1. For example, 2, 3 and 4 are consecutive integers.

For this problem:
Let the first =x

Let the second integer =x+1

Let the third integer =x+2

Let the fourth integer =x+3

The sum of the 2nd and 4th is
#x+1color(white)(aaa)+color(white)(aaa)x+3#

#x+1+x+3=132#

Combine like terms

#2x+4=132#

Subtract 4 from both sides.

#2x+4-4=132-4#
#2x=128#

Divide both sides by 2.
#(2x)/2=128/2#
#x=64#

The first integer is 64.
The 2nd is 65.
The 3rd is 66.
The 4th is 67.