Question

21 Maria sold small boxes of candy for $1 and

Answer 1

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 $y$ and an Independent variable $x$. 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 $y$ and $x$ 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:

• Small Boxes (lets call them $s$) cost $1 per box

• Large Boxes (lets call them $l$) 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:

$s+l=30$        Eqn(1): Total Number of Boxes

$1s+4l=60$     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, $s$ and $l$ respectively.

From Eqn(1) we see that

$s=30-l$      Eqn(3).

Plugging Eqn(3) in Eqn(2) we can solve for $l$ as:

$1(30-l)+4l=60$

$30-l+4l=60$       Factored out bracket

$3l=60-30$          Gather similar terms on each side and simplify

$3l=30$

$l=\frac{30}{3}$

$l=10$

Plugging in the value for $l=10$ in Eqn(3) we have

$s=30-10\\s=20$

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.