Question

The sum of three consecutive
odd numbers is 45. Find the numbers.
*​

Answer 1

Answer:

Step-by-step explanation:

If you have to use algebra, then choosing the setup can make your life a lot easier. What if we set it up like;

(X-2) + X + (X+2) =45

3X=45

X=15

You don’t have to designate that they are odd in the equation because three even numbers can’t sum to an odd number.

Answer 2

Answer:

Let n = a number and 2n = an even number, then ...

Let 2n + 1 = the first of three consecutive odd numbers.

Let 2n + 3 = the second of three consecutive numbers.

Let 2n + 5 = the third of three consecutive odd numbers.

Since it's given that the sum of our three consecutive odd numbers is 45, then we can write the following equation to be solved for the variable n:

(2n + 1) + (2n + 3) + (2n + 5) = 45

2n + 1 + 2n + 3 + 2n + 5 = 45

Collecting like-terms on the left, we get:

6n + 9 = 45

Now, subtracting 9 from both sides in order to begin isolating the unknown, n, on the left side:

6n + 9 - 9 = 45 - 9

6n + 0 = 36

6n = 36

Now, divide both sides by 6 in order to solve the equation for n:

(6n)/6 = 36/6

(6/6)n = 36/6

(1)n = 6

n = 6

Therefore, ...

2n + 1 = 2(6) + 1

= 12 + 1

= 13

2n + 3 = 2(6) + 3

= 12 + 3

= 15

2n + 5 = 2(6) + 5

= 12 + 5

= 17

CHECK:

(2n + 1) + (2n + 3) + (2n + 5) = 45

(13) + (15) + (17) = 45

13 + 15 + 17 = 45

45 = 45..

Hope it helps you..