The sum of two consecutive odd integers is sixteen more than #4# times the smaller integer. What are the two integers?

2 Answers
Oct 18, 2017

-7 and -5

Explanation:

Translate the sentence into maths.

sum of two consecutive odd integers means #a + (a+2)# because consecutive is the next one, and odd numbers are 2 apart.

This sum... is sixteen more than 4 times the smaller integer
So #a+(a+2)=16+ (a*4)#

Now solve for #a#

#a + (a+2) = 4a +16#
#2a+2=4a+16#
#-14=2a#
#a=-7#

#:. a=-7, -5#

Oct 18, 2017

The smaller is #-9# and the larger #-11#

Explanation:

Denote the smaller integer by #n#

If #n > 0# then the larger integer is #n+2# and:

#n+(n+2) = 4n+16#

That is:

#2n+2 = 4n+16#

Subtracting #2n+16# from both sides:

#-14 = 2n#

Hence

#color(red)(cancel(color(black)(n = -7)))#

If #n < 0# then the larger integer is #n-2# and:

#n+(n-2) = 4n+16#

That is:

#2n-2 = 4n+16#

Subtracting #2n+16# from both sides:

#-18 = 2n#

Hence:

#n = -9#