Question

How do you find two consecutive integers where the sum is 223?

Answer 1

Hint: In the given question, we have been given that there are two consecutive integers. Their sum is given to be 223. We have to find the value of the integers. To do that, we express one of the integers in the form of the other integer – we are going to assume the value of one integer and express the other in the form of that one integer. And then we solve and find the value of the integers.

Complete step-by-step answer:
Let the smaller integer be \[x\].
Then, since the other integer is consecutive, it equals \[x + 1\].
Now, we have the three numbers: \[x - 2,x,x + 2\].
Given, their sum is \[223\].
Hence, \[x + x + 1 = 223 \Rightarrow 2x + 1 = 223 \Rightarrow 2x = 222 \Rightarrow x = 111\]
So, the smaller number is \[111\].
Thus, the other number is \[111 + 1 = 112\].
Hence, the two numbers are \[111\] and \[112\].

Additional Information:
Here, we were given two integers which followed a pattern in their difference – they differed by \[1\]. But if there were three of such then that system of the given numbers, where the difference between three or more numbers is equal is called an arithmetic progression. The arithmetic progression is used in such things only, for finding the integers when the numbers are quite big, and when we have to find the sum of such integers.

Note: In the given question, we had to find the value of the two consecutive integers whose sum is given. To do that, we assumed the value of one integer and expressed the other in the form of that one integer. And then we solved and found the value of the integers. So, it is really important that we know the formulae and where, when and how to use them so that we can get the correct result.