use equations to solve word problems

Question

the sum of three consecutive odd integers is 93. find the integers.

Answer 1

You could also consider the following solution. Let n = the middle integer. Then the lower integer will be n - 2, and the higher will be n + 2. Adding all 3 integers gives 3n, since + 2 and - 2 cancel each other.

3n = 93, n = 31. The lower is 29, and higher is 33.

Answer 2

If "n" is any integer, to make sure you get an odd number you can multiply it by 2 and then add 1. Multiplying any number by 2 makes it an even number and 1 more than any even number will be an odd number. So, "2n + 1" always results in an odd number no matter what you pick for "n".

So our first odd number will be "2n + 1". The our 2nd odd number will be "2n + 3" and our third odd number will be "2n + 5"

The sum is 93 means:

(2n + 1) + (2n + 3) + (2n + 5) = 93

6n + 9 = 93

6n = 84

n = 14

So, the first odd number is 2(14) + 1 = 29. The next would be 31, the next would be 33,

29, 31, 33