Finding the Smallest Consecutive Odd Number

The problem asks us to find the smallest number among four consecutive odd numbers whose sum is 160.

Algebraic Representation

Let the smallest odd number be represented by the variable $x$. Since the numbers are consecutive odd numbers, they increase by 2 each time. Therefore, the four consecutive odd numbers can be represented as:

• First number: $x$
• Second number: $x+2$
• Third number: $x+4$
• Fourth number: $x+6$

Setting Up the Equation

The problem states that the sum of these four numbers is 160. We can write this as an equation:

$x + (x+2) + (x+4) + (x+6) = 160$

Solving the Equation

Combine the terms involving $x$ and the constant terms:

$4x + 12 = 160$

Subtract 12 from both sides of the equation to isolate the term with $x$:

$4x = 160 - 12$

$4x = 148$

Divide both sides by 4 to find the value of $x$:

$x = \frac{148}{4}$

$x = 37$

Identifying the Smallest Number

Since $x$ was defined as the smallest odd number in the sequence, the smallest number is 37.

Verification (Optional)

The four consecutive odd numbers are 37, 37+2=39, 37+4=41, and 37+6=43. Let's check their sum:

$37 + 39 + 41 + 43 = 160$

The sum is indeed 160, confirming our result.