Q44. - 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 $\$ 15,000$. 

$44.$ How many laser printers and how many color monitors were delivered?

Step-by-Step Solution

Answer

There are $18$ laser printers and $12$ color monitors.

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

Here, x represents the number of boxes of laser printers and y represents the number of boxes of color monitors. The equations so formed according to the question are:

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

Step-3 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-4 – Solving one equation for x in terms of y

To solve the equation $x+y=30$ for x in terms of y, subtract y from both sides as shown below.

$\begin{array}{c}x+y-y=30-y\\ x=30-y\end{array}$

Step-5 – Substitute the expression

Now, substitute $x=30-y$ in the equation $7x+2y=150$ and solve.

$\begin{array}{c}7\left(30-y\right)+2y=150\\ 210-7y+2y=150\\ -5y=-60\\ y=12\end{array}$

Thus, the value of y is $12$.

Step-6 – Substitute the value of variable

To find the value of x, substitute $y=12$ in the equation $x+y=30$ and then solve as shown.

$\begin{array}{c}x+y=30\\ x+12=30\\ x=30-12\\ x=18\end{array}$

Thus, the value of x is $18$.

Hence, there are $18$ laser printers and $12$ color monitors.