Write a linear system of equations. Let x be the number of inkjet​ printers, y be the number of LCD​ monitors, and z be the number of memory chips. Choose the correct answer below.

Question

A company is upgrading office technology by purchasing inkjet​ printers, LCD​ monitors, and additional memory chips. The total number of pieces of hardware purchased is

48.

The cost of each inkjet printer is

​$107​,

the cost of each LCD monitor is

​$130​,

and the cost of each memory chip is

​$90.

The total amount of money spent on new hardware came to

​$4993.

They purchased two times as many memory chips as they did LCD monitors. Determine the number of each that was purchased.

Answer 1

Let the inkjet printer be X (costing ​$107​)

Let the LCD monitor be Y (costing ​$130​)

Let the memory chips be Z (costing $90)

We know the there were only 48 pieces of hardware purchased, so we can state the following

X + Y + Z = 48

We also know the total amount of money spent on new hardware came to ​$4993, so that

107X + 130Y +90Z = 4993

Since they purchased two times as many memory chips as they did LCD monitors, we can substitute 2Y for the variable Z. Resulting in

X + Y + 2Y = 48 or X+ 3Y = 48 and

107X + 130Y + 90(2Y) = 4993 Distribute the parenthesis to get

107X +130Y + 180Y = 4993 or 107X + 310Y = 4993

Now we have two variables (X&Y) so it's easier to solve. The equations are

X+ 3Y = 48

107X + 310Y = 4993

You can use either the substitution method or the elimination method to solve. I find the elimination method to be easiest. Multiply one of the equations so that one of the variables cancels out. If we multiply the first equation by -107, it will cancel out the X variable.

[X+ 3Y = 48] x (-107) which results in -107X - 321Y = -5,136

-107X -321Y = -5,136 then add the equations together and you are left with

+ 107X + 310Y = 4993

0 -11Y = -143 then divide both sides by -11 and the Y variable is 13.

So they bought 13 LCD monitor's, 26 memory chips (twice as many as the LCD Monitors), and 9 Inkjet Printers (48 - 13 - 26 = 9).