Question

Three consecutive odd numbersadd up to 177.For the above word problem, write the VARIABLE REPRESENTATION foreach of the three numbers in this sequence. Use the variable representation of the three numbers to write theequation used to solve the above word problem. What is the SECOND number in this sequence of three consecutivenumbers?

Answer 1

Given:

Three consecutive odd numbers add up to 177.

We know the difference between the consecutive odd numbers is 2.

To represent the word problem above, let x represent the first odd number in the sequence.

The variable representation for each number:

First odd number = x

Second odd number = x + 2

Third odd number = x + 2 + 2

We have the equation to solve the word problem:

(x) + (x + 2) + (x + 2 + 2) = 177

Let's solve for x:

x + x + 2 + x + 2 + 2 = 177

Combine like terms:

x + x + x + 2 + 2 + 2 = 177

3x + 6 = 177

Subtract 6 from both sides:

3x + 6 - 6 = 177 - 6

3x = 171

Divide both sides by 3:

`\begin{gathered} (3x)/(3)=(171)/(3) \\ \\ x=57 \end{gathered}`

Let's find the second number:

Second number = x + 2

Substitute x for 57:

Second number = x + 2

= 57 + 2 = 59

Therefore, the second number in his sequence of threee consecutive numbers is 59

ANSWER:

Second number = 59