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# The sum of three consecutive integers is 258. How do you find three integers?

Last updated date: 16th Jul 2024
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Hint:We are given with the sum of three consecutive integers and asked to find the three consecutive integers, so assume one of them as ‘x’ and others as ‘x+1’ and ‘x+2’. Add these three integers and equalize with the given sum which is 258, to find the value of ‘x’ and other integers can also be found using ‘x+1’ and ‘x+2’.

Complete step by step solution:
Firstly, we should know the meaning of consecutive integers. These are those integers which come one after another like successive numbers or may be defined as numbers which follow each other in order.
For example,
1, 2, 3 is a set of three consecutive integers, or -2,-1, 0 or 60, 61, 62.
Given that, the sum of three consecutive integers is 258. Let us assume that ‘x’ is one of the consecutive
integer, then other two consecutive integers would be ‘x+1’ and ‘x+2’.
$\therefore$x, x+1, x+2 is a set of three consecutive integers whose sum is 258.
$\Rightarrow x + (x + 1) + (x + 2) = 258 \\ \Rightarrow x + x + 1 + x + 2 = 258 \\ \Rightarrow 3x + 3 = 258 \\ \Rightarrow 3(x + 1) = 258 \\ \Rightarrow x + 1 = \dfrac{{258}}{3} \\ \Rightarrow x + 1 = 86 \\ \Rightarrow x = 86 - 1 \\ \Rightarrow x = 85 \\$
Therefore, one of the consecutive integers is 85. Then, the other two integers would be 86 and 87.
Hence, 85, 86, 87 is a set of three consecutive integers whose sum is 258.

Note:We can also assume x-1, x, x+1 as the set of three consecutive integers and then determine the value of x by using the simple algebraic addition, $(x - 1) + x + (x + 1) = 258$. In this case, we would get the value of $x = 86$, $x - 1 = 85$ and $x + 1 = 87$. Hence, we get the same set of consecutive integers.