Question

find three consecutive odd integers such that the sum of the first and the third equals the sum of the second and 13

Answer 1

Answer: The three odd integers are 11, 13 and 15.

Step-by-step explanation: The first point to note is that the three unknown numbers are consecutive, which means they follow one after the other. Also we are told that the numbers are consecutive “odd integers.” This also means there is a two-digit interval between one number and the next. Hence, if the first number is A, the next number will be A + 2, and the third number will be A + 2 + 2 (that is, A + 4)

At this point we can now derive the following expressions based on the information we have been given, which is;

The sum of the first and third (A + {A + 4} )equals the sum of the second and 13 ({A + 2} + 13). Therefore we can write this out as follows;

A + {A + 4} = {A + 2} + 13

After removing brackets we now have

A + A + 4 = A + 2 + 13

2A + 4 = A + 15

By collecting like terms we now have

2A - A = 15 - 4

(Remember that when a positive value crosses to the other side of the equation it becomes negative, and vice versa)

2A - A = 15 - 4

A = 11

Hence, the three consecutive integers are 11, 13 and 15.