Question

The sum of three consecutive integers is 45. Find the integers.

Answer 1

Hint: In this question, first of all assume three consecutive integers as x, (x + 1) and (x + 2). Now, add them and equate to 45 and find the value of x from the equation, and from x, find the three consecutive integers.

Complete step-by-step answer:
Here, we are given that the sum of 3 consecutive integers is 45, we have to find the integers. Let us consider that our first integer is x. We know that the consecutive numbers differ by 1. So, let us take the next consecutive integer as (x + 1). Now again the next consecutive integer would differ by 1 from the previous integer. So, we take the third integer as (x + 2). Hence, we get,
Value of the first integer = x …. (i)
Value of the second integer = x + 1 ….. (ii)
Value of the third integer = x + 2 ….. (iii)
Now, we are given that the sum of three consecutive integers is 45. So, we get,
(First Integer) + (second Integer) + (Third Integer) = 45
By substituting the value of the first, second and third integers from equation (i), (ii) and (iii) respectively, we get,
(x) + (x + 1) + (x + 2) = 45
By rearranging the terms of the above equation, we get,
(x + x + x) + (1 + 2) = 45
3x + 3 = 45
By subtracting 3 from both sides of the above equation we get,
3x = 45 – 3
3x = 42
By dividing by 3 on both the sides of the above equation, we get,
\[x=\dfrac{42}{3}\]
x = 14
So, we get the value of the first integer = x = 14
Value of the second integer = x + 1 = 15
Value of the third integer = x + 2 = 16

Note: In these questions, students can verify their answer by adding 14, 15, and 16 and checking if the value of the sum is equal to 45 or not. Also, in this question, some students take 3 consecutive numbers as (x + 1), (x + 2) and (x + 3) after adding them and equating to 45, they get x = 13. So, they take three consecutive numbers as 13, 14, and 15 which is wrong because their first number should be x + 1 = 13 + 1 = 14 and the next numbers as 15 and 16. So, this must be taken care of.