Answer:
There where 10 more Small boxes sold than Large boxes.
Step-by-step explanation:
This is a typical question that can be solved by obtaining a system of two linear equations and solving for each variable.
In principle Linear Equations are algebraic expressions denoting a relationship between a Dependent variable [tex]y[/tex] and an Independent variable [tex]x[/tex]. In a system of Two Linear equations we have two equations of the same variable sets (thus Two Independent variables) so in this case both [tex]y[/tex] and [tex]x[/tex] will be variable terms.
Now with respect to the question and the given information, here our two Variable terms will be the small and the large boxes.
Given Information:
Thus from the above we can obtain one equation denoting the Total Number of Boxes sold and one equation denoting the Total Profit from sold boxes, respectively, as follow:
[tex]s+l=30[/tex] Eqn(1): Total Number of Boxes
[tex]1s+4l=60[/tex] Eqn(2): Total Profit from sold boxes
Now we have a system of two linear equations which we can solve and find the number of small and large boxes, [tex]s[/tex] and [tex]l[/tex] respectively.
From Eqn(1) we see that
[tex]s=30-l[/tex] Eqn(3).
Plugging Eqn(3) in Eqn(2) we can solve for [tex]l[/tex] as:
[tex]1(30-l)+4l=60[/tex]
[tex]30-l+4l=60[/tex] Factored out bracket
[tex]3l=60-30[/tex] Gather similar terms on each side and simplify
[tex]3l=30[/tex]
[tex]l=\frac{30}{3}[/tex]
[tex]l=10[/tex]
Plugging in the value for [tex]l=10[/tex] in Eqn(3) we have
[tex]s=30-10\\s=20[/tex]
So we know that they were 10 Large Boxes and 20 Small Boxes sold, thus to answer our question, there where 10 more Small boxes sold than Large boxes.
