- #1

down to earth

- 6

- 3

## Homework Statement

The larger of two numbers exceeds twice the smaller number by ##8##. The sum of twice the larger and ##3## times the smaller number is ##65##. If ##x## is the smaller number, which equation below determines the correct value of ##x##?

A. ##3(2x+8)+2x=65##

B. ##3(2x-8)+2x=65##

C. ##(4x+8)+3x=65##

D. ##2(2x+8)+3x=65##

E. ##2(2x-8)+3x=65##

B. ##3(2x-8)+2x=65##

C. ##(4x+8)+3x=65##

D. ##2(2x+8)+3x=65##

E. ##2(2x-8)+3x=65##

(According to the book, the correct answer is D.)

2. Homework Equations

2. Homework Equations

To be consistent with the book, I'll let the larger number be ##y##, and the smaller number be ##x##.

## The Attempt at a Solution

Taking this one step at a time:

*The larger of two numbers exceeds twice the smaller number by ##8##.*

I think this translates into ##y+8=2x##.

*The sum of twice the larger and ##3## times the smaller number is ##65##.*

So this means that ##2y+3x=65##. Now, because they want the answer to be in terms of ##x##, I need to rewrite ##y## in terms of ##x## (which is ##y=2x-8##) and plug that into the formula.

Then it becomes ##2(2x-8)+3x=65##. This is answer option E, but apparently this is isn't the right answer.

Please, look over my steps and see if you can spot what I missed. The correct answer, D, differs only by the sign inside the parenthesis. I don't see what I'm doing wrong, and I'm really confused as to how they got ##+8##. Thank you.