The sum of two consecutive odd integers is sixteen more than 44 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)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)a+(a+2)=16+(a4)

Now solve for aa

a + (a+2) = 4a +16a+(a+2)=4a+16
2a+2=4a+162a+2=4a+16
-14=2a14=2a
a=-7a=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