Question

21 Maria sold small boxes of candy for $1 and

large boxes for $4. She sold a total of 30
boxes for $60. How many more small
boxes did she sell?

Answer 1

There where 10 more Small boxes sold than Large boxes.

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=(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.