Does Textbook Question have wrong answer? Grade 9 Algebra. My son had this question for his homework. I am following along refreshing myself so he will have someone to come to for help or just to talk about maths if he decides to keep on it through school. Anyway I got a different answer to the book answer for this question. 
At the start of lunch, Jimmy and Jake each brought out a new bag of x marbles to play with their friends. By the end of lunch they were surprised to see they still had the same total number as before even though overall Jimmy had gained 5 marbles and Jake had ended up with two lots of 3 less than his original amount. How many marbles were originally in each bag?  
I got 1, the book answer says 11. 
 A: *

*Jimmy had $x$ marbles and gained $5$, so Jimmy has $x+5$ marbles after lunch. 

*Jake had $x$ marbles. A "lot of $3$ less than his original amount" would be $x−3$, but he has two such lots; thus, Jake has $2(x−3)$ marbles after lunch. 

*If, as the problem states, Jimmy and Jake "still had the same total number as before", then the after-lunch total is the same as the original total: 
$$x+5 + 2(x-3) = x+x \quad\to\quad x+5 + 2x-6 = 2x  \quad\to\quad x = 1 \tag{1}$$ But, then, each of Jake's "lot of $3$ less" would be $x-3=1-3=-2$ marbles, so that his two lots are $-4$. It's unlikely-in-the-extreme that the problem intends for Jake to "end up with" negatively-many marbles.

*If, instead, the problem had stated that Jimmy and Jake, say, "still had equal numbers of marbles", then we'd have
$$x+5=2(x-3)\quad\to\quad x+5=2x-6\quad\to\quad 11 = x \tag{2}$$ This checks out: After lunch, Jimmy has $11+5=16$ marbles, and Jake has $2(11-3)=2\cdot8=16$ marbles. However, it's hard to see "still had the same total number as before" as a typo or otherwise poor phrasing of "still had equal numbers of marbles". (And yet, that's how I'd initially mis-read the problem when I posted a comment with the $x=11$ solution. :)
So, there's a path to $x=1$ and a path to $x=11$, neither of which is really satisfactory. Take it up with the author, I guess. :)
A: So you have to make an equation.
Let the original amount of marbles = x.
Since Jimmy gained 5 marbles, you add 5 to the original amount of marbles, therefore we have x+5
Then it says that Jake gained double of 3 less than the original amount, which creates the equation 2(x-3)
STEP 1:
And since it also states that they are an equal amount, the equation would be written as the following:
x+5=2(x-3)
STEP 2:
Then you expand
x+5=2x-6
STEP 3:
Following the steps of linear equations and the inverse method you would have to solve for x as the following:
x+5-2x=-6
This is due to the fact that 2x is positive, so it would turn negative if you wanted to put it on the opposite side. You could start with any of the numbers, whether it be the 5, x, 6 or 2x as I did, but I did it this way due to the fact that I like to put all the x’s on the left side. The equation will end up a little different and I’ll show how to do it starting with each of the values and how they give the same answer.
STEP 4:
Then you put the 5 on the right side (still following inverse equations)
x-2x=-6-5
STEP 5:
Then solve
-x=-11
STEP 6:
x=11
Since you can’t have a negative x value, multiply both sides by -1
There you go! 11. Hope that makes sense. Below i’ll show the process of starting with the other numbers to show how they differ. I will not be providing an explanation though lol. Though, if you understand inverse equations, and this cleared up some confusion, the rest may not benefit you.
STARTING WITH 2x (WITHOUT EXPLANATION
x+5=2(x-3) —>
x+5=2x-6 —>
x+5-2x=-6  —>
x-2x=-6-5  —>
-x=-11  —>
x=11
STARTING WITH 5
x+5=2(x-3)  —>
x+5=2x-6   —>
x=2x-6-5   —>
x-2x=-6-5   —>
-x=-11   —>
x=11
STARTING WITH 6
x+5=2(x-3)   —>
x+5=2x-6   —>
x+5+6=2x   —>
5+6=2x-x   —>
11=x   —>
(x=11)
STARTING WITH X
x+5=2(x-3)   —>
x+5=2x-6   —>
5=2x-6-x   —>
5+6=2x-x   —>
11=x   —>
(x=11)
HOPE THAT HELPED :)
