Question

The sum of 4 consecutive odd integers is 336, how do you find the largest integer?

Answer 1

Hint:In the question, we are given that the sum of 4 odd consecutive integers is 336. So assume one integer as ‘x’ and others as \[x + 2,\,x + 4,\,x + 6\] because odd consecutive integers differ from each other by 4. Value of x can be determined by adding up assumed terms and equating it with 336. And by value of x other integers can also be calculated and in this way we would get the largest integer as well.

Complete step by step solution:
Given that, the sum of 4 consecutive odd integers is 336. Let us assume that ‘x’ is one of the consecutive odd integers, then another consecutive odd integer would be \[x + 2,\,x + 4,\,x + 6\] because odd consecutive integers differ by 2.
\[
\Rightarrow x + (x + 2) + (x + 4) + (x + 6) = 336 \\
\Rightarrow x + x + 2 + x + 4 + x + 6 = 336 \\
\]
Add the variables and constants together,
\[ \Rightarrow 4x + 12 = 336\]
Shifting all the constants at one side by changing signs:
\[
\Rightarrow 4x = 336 - 12 \\
\Rightarrow 4x = 324 \\
\Rightarrow x = 81 \\
\]
Thus, one of the odd integer would be 81, the other odd consecutive integers would be given by:
\[
x + 2 = 81 + 2 = 83 \\
x + 2 = 83 + 2 = 85 \\
x + 2 = 85 + 2 = 87 \\
\]
Hence, the four consecutive odd integers whose sum is336 are: \[81,\,83,\,85\,and\,87\]. But in the question we were asked to find the largest in those four integers which is 87.

Note: 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, and
Now, consecutive odd integers are those numbers which follow each other in order and differ by 2.
For example,
1, 3, 5 is a set of three consecutive odd integers.
Similarly, -51, -53, -55 is another set of three consecutive odd integers.
Now, consecutive positive even numbers are those numbers which are greater than 0 and which follow each other in order and differ by 2.
For example,
2, 4, 6 is a set of three consecutive positive even integers.
Similarly, 52, 54, 56 is another set of three consecutive positive even integers.