The ratio of 7th grade students to 8th students in a soccer league is 17:23. If there are 200 students in all, how many are in t
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Answer:
There where 10 <u>more</u> Small boxes sold than Large boxes.
Step-by-step explanation:
<u>This is a typical question that can be solved by obtaining a system of two linear equations and solving for each variable. </u>
In principle Linear Equations are algebraic expressions denoting a relationship between a Dependent variable and an Independent variable
. In a system of Two Linear equations we have<u> two equations</u> of the same variable sets (thus Two Independent variables) so in this case both
and
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.
<u>Given Information:</u>
- Small Boxes (lets call them
) cost $1 per box
- Large Boxes (lets call them
) cost $4 per box
- Total Number of Boxes sold is 30
- Total Profit from sold Boxes is $60
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:
Eqn(1): Total Number of Boxes
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, and
respectively.
From Eqn(1) we see that
Eqn(3).
Plugging Eqn(3) in Eqn(2) we can solve for as:
Factored out bracket
Gather similar terms on each side and simplify
Plugging in the value for in Eqn(3) we have
So we know that they were<u> 10 Large Boxes and 20 Small Boxes sold</u>, thus to answer our question, there where 10 more Small boxes sold than Large boxes.