three consectutive odd integers

Question

Find three consecutive odd integers such that the sum of the first two is nine more than the third integer.

Answer 1

Use key words to piece together an equation.

1. Consecutive odd integers hints that you will need to use (2n+1), (2n+3), and (2n+5) somewhere in the equation
2. Whose sum is 9 more than the third integer. This hints that you will have to add 9 somewhere in this equation

So let's try and set this up. My first guess is something along the lines of:

(2n+1)+(2n+3)=(2n+5)+9. This gives me my sum of the first two integers is equal to 9 more than the third. Let's simplify and solve for n.

2n+1+2n+3=2n+5+9

4n+4=2n+14

2n=10

n=5

Now that we have our n, we can plug that back in to get our three consecutive integers.

(2(5)+1)=11

(2(5)+3)=13

(2(5)+5)=15

Does 11+13 equal 9 more than 15?

11+13=24

24-15=9

Yes!

Therefore, our integers are 11,13, and 15.