Question

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

Answer 1

Hi,

15

Explanation:

The three consecutive odd integers are : 2k+1,2k+3,2k+5

Since 3*(2k+1)=3+2*(2k+5) then

6k+3=3+4k+10

2k=10

k=5

and 2k+5=2*5+5=5

The three numbers are 11,13,15

Answer 2

15

Explanation:

Let's solve this step by step:

Let the first odd integer be "x."

The three consecutive odd integers are then: x, x + 2, and x + 4 (since odd integers are separated by 2).

Now, we can set up the equation based on the given information:

Three times the first integer (3x) is 3 more than twice the third integer (2(x + 4) + 3):

3x = 2(x + 4) + 3

Now, solve for x:

3x = 2x + 8 + 3

3x = 2x + 11

3x - 2x = 11

x = 11

So, the first odd integer is x = 11, and the three consecutive odd integers are 11, 13, and 15.

The third odd integer is x + 4, which is 11 + 4 = 15. Therefore, the third integer is 15.