Solve ACT Word Problem: Find Value of x

[down to earth]

I'm studying for the ACT and this was one of the practice test problems. The book does offer an explanation for how to get the answer but it isn't very detailed and I still don't know what I'm doing wrong.

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. $2(2x-8)+3x=65$​

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

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.

 

[PeroK]

If $y$ exceeds $2x$ by $8$ then $y = 2x + 8$.

 

[down to earth]

If $y$ exceeds $2x$ by $8$ then $y = 2x + 8$.

Ohh... so I must've messed up at the first step then. I think I see what I did wrong now: to show that $y$ was greater than $2x$ by $8$, I should have added the 8 on the other side of the equation. Dumb mistake on my part. Thanks!