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A number is 8 less than 6 times a second number. Their sum is 156. If [tex]x[/tex] represents the second number, which equation is correct to find the two numbers?

Choose the correct answer below.

A. [tex](6x + 8) - x = 156[/tex]
B. [tex](8x + 6) - x = 156[/tex]
C. [tex](8x - 6) + x = 156[/tex]
D. [tex](6x - 8) + x = 156[/tex]

Answer :

To solve this problem, we need to find which equation correctly represents the relationship between the two numbers.

Let's break down the information provided in the problem:

1. We have two numbers: the first number and the second number. We'll use [tex]\( x \)[/tex] to represent the second number.

2. The statement "A number is 8 less than 6 times a second number" can be translated into an expression for the first number:
- The first number = [tex]\( 6x - 8 \)[/tex].

3. We know that the sum of the two numbers is 156:
- The first number + the second number = 156.
- So, [tex]\( (6x - 8) + x = 156 \)[/tex].

Now, let's simplify this equation step-by-step:

1. Combine like terms:
- [tex]\( (6x - 8) + x = 6x + x - 8 \)[/tex].
- Which simplifies to [tex]\( 7x - 8 \)[/tex].

2. Set up the equation with the sum:
- We have [tex]\( 7x - 8 = 156 \)[/tex].

This is the equation that represents the relationship between the two numbers based on the conditions given in the problem.

Therefore, the correct option is:

D. [tex]\((6x - 8) + x = 156\)[/tex]

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