Q43. - Algebra 2

Question

Heung-Soo is responsible for checking a shipment of technology equipment that contains laser printers that cost $\backslash ( 700$ each and color monitors that cost $\backslash ) 200$ each. He counts $30$ boxes on the loading dock. The invoice states that the order totals$\$ 15,000$.

Write a system of two equations that represents the number of each item.

Step-by-Step Solution

Answer

The equations so formed for the given question is  $\begin{array}{c}x+y=30\\ 7x+2y=150\end{array}$

Step-1 – Apply the concept of system of equations

A set of two or more equations with the same variables is called a system of linear equations. The ordered pairs that satisfy all the equations in the system is called as solution of the equations.

Step-2 – Formation of the equations

Let us suppose the number of boxes of laser printers be x and the number of boxes of color monitors be y.

Now according to the question, the total number of boxes are $30$.

The first equation so formed is below.

$x+y=30$

Step-3 – Formation of the equations

Consider the second statement.

The invoice states the order total to be of $\$ 15,000$. The cost of each laser printer is $\$ 700$ and that of color monitor is $\$ 200$, which is mathematically expressed in the equation as shown.

$\begin{array}{c}700x+200y=15,000\\ 7x+2y=150\end{array}$

Hence, both the equations so formed for the given question are 

$\begin{array}{c}x+y=30\\ 7x+2y=150\end{array}$