# Math Help - Systems of Equations application problem

1. ## Systems of Equations application problem

I'm not sure how to even begin to solve this:
You have boxes of five types. They are characterized by their length , their width , their height , their age , and their price , as given in the following table:

So for example, boxes of type IV measure 1 by 2 by 4 feet, are a year old, and cost $2.- each. Suppose the sum of the lengths of your boxes is 30, the sum of their widths 49, the sum of their heights 87, the sum of their ages 40, and the total price of those boxes 55. You have boxes of type I_____ boxes of type II_____ boxes of type III_____ boxes of type IV_____ boxes of type V______ Do the numbers corresponding to the length, height, width, sum and price go on the right hand side of the system, and then just solve? e.g.1 1 1 1 1 = 30 1 1 2 3 2 = 49 1 2 3 2 2 = 87 1 2 4 1 2 = 40 1 2 3 1 3 = 55 2. Originally Posted by thebristolsound I'm not sure how to even begin to solve this: You have boxes of five types. They are characterized by their length , their width , their height , their age , and their price , as given in the following table: So for example, boxes of type IV measure 1 by 2 by 4 feet, are a year old, and cost$ 2.- each. Suppose the sum of the lengths of your boxes is 30, the sum of their widths 49, the sum of their heights 87, the sum of their ages 40, and the total price of those boxes 55.
You have

boxes of type I_____
boxes of type II_____
boxes of type III_____
boxes of type IV_____
boxes of type V______

Do the numbers corresponding to the length, height, width, sum and price go on the right hand side of the system, and then just solve?

e.g.1 1 1 1 1 = 30
1 1 2 3 2 = 49
1 2 3 2 2 = 87
1 2 4 1 2 = 40
1 2 3 1 3 = 55
As it is right now, you're adding up different characteristics for individual boxes. You want to add up the same characteristic for different boxes, so you want this matrix:

$\left[\begin{array}{cccccc}1&1&1&1&1&30\\1&1&2&2&2&49\\1 &2&3&4&5&87\\1&3&2&1&1&40\\1&2&2&2&3&55\end{array} \right]$

3. Originally Posted by thebristolsound
I'm not sure how to even begin to solve this:
You have boxes of five types. They are characterized by their length , their width , their height , their age , and their price , as given in the following table:

So for example, boxes of type IV measure 1 by 2 by 4 feet, are a year old, and cost \$ 2.- each. Suppose the sum of the lengths of your boxes is 30, the sum of their widths 49, the sum of their heights 87, the sum of their ages 40, and the total price of those boxes 55.
You have

boxes of type I_____
boxes of type II_____
boxes of type III_____
boxes of type IV_____
boxes of type V______

Do the numbers corresponding to the length, height, width, sum and price go on the right hand side of the system, and then just solve?

e.g.1 1 1 1 1 = 30
1 1 2 3 2 = 49
1 2 3 2 2 = 87
1 2 4 1 2 = 40
1 2 3 1 3 = 55
Let the number of each type that you have be $x_{I},\ x_{II},\ x_{III},\ x_{IV},\ x_V$ then each of the conditions gives a equation, for example the sum of the prices is $55$ gives:

$1 x_I+ 2 x_{II} + 3 x_{III} + 4 x_{IV}+5 x_V =55$

each of the other conditions gives another equation. This gives you a system of equations that you then solve for the $x$'s

CB