To solve this problem, we can write an equation letting the variable x represent the number of bottles in a box of water (this means that the expression x-1 represents the boxes that have one fewer bottle than a full box).
This allows us to create the following equation:
9 original bottles + 3x (3 full boxes) + 2(x-1) (two boxes with one fewer bottle) = 67 total bottles
OR
9 + 3x + 2(x-1) = 67
Now, we can begin to solve this equation by using the distributive property to get rid of the parentheses on the left side of the equation.
9 + 3x + 2x - 2 = 67
Next, we can combine like terms on the left side of the equation (meaning add the variable terms together and subtract the constant terms).
7 + 5x = 67
Now, we should subtract 7 from both sides of the equation to get the variable term alone on the left side of the equation.
5x = 60
Next, we should divide both sides by 5 to isolate the variable x on the left side of the equation.
x = 12
Therefore, your answer is that there are 12 bottles in a full box.
Hope this helps!