Question

How do you find two consecutive odd integers whose sum is $56?$

Answer 1

Hint: Consecutive numbers can be defined as the numbers which follow each other in order from the smallest to the largest number. Odd numbers are the numbers which are not completely divisible by two. Here we will assume the unknown consecutive odd numbers using variables and frame the equation and simplify for the required values.

Complete step-by-step answer:
Let us assume that two consecutive odd integers be $(x + 1)$and $(x + 3)$
Given that sum of two odd consecutive numbers is $56$
Frame the given word statement in the form of the mathematical expression.
$(x + 1) + (x + 3) = 56$
Open the brackets in the above expression –
$x + 1 + x + 3 = 56$
Combine the like terms in the above expression –
$\underline {x + x} + \underline {1 + 3} = 56$
Simplify the like terms in the above expression –
$2x + 4 = 56$
Make the required term the subject and move other terms on the opposite side. When you move any term from one side to the opposite side then the sign of the terms also changes. Positive term becomes negative and vice-versa.
$2x = 56 - 4$
Simplify the above expression finding the difference of the terms –
$2x = 52$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$x = \dfrac{{52}}{2}$
Find the factors of the term in the numerator of the above expression –
$x = \dfrac{{26 \times 2}}{2}$
Common factors from the numerator and the denominator cancel each other.
$x = 26$
Hence, the required numbers are –
$x + 1 = 26 + 1 = 27$ and
$x + 3 = 26 + 3 = 29$
So, the correct answer is “ 27, 29”.

Note: Always remember that the difference between two consecutive numbers is always fixed and they follow some pattern. Be careful while framing the first equation from the given word statements and verify the resultant value with it. The first mathematical form of the given data is the most important step and so be wise to frame it.