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 49. The cost of each inkjet printer is $106, the cost of each LCD monitor is $131, and the cost of each memory chip is $83. The total amount of money spent on new hardware came to $4921. They purchased two times as many memory chips as they did LCD monitors. Determine the number of each that was purchased. 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. A. X+49y+832 = 4921 X+ y + z = 131 - 2y + z = 106 B. 106x + 832 = 4921 x + y + z = 49 - 2y + z = 0 106x + 131y + 832 = 4921 x + y + 2z = 49 - 2y + z = 33 D. 106x + 131y+83z = 4921 X + y + z = 49 - 2y + z = 0 The company purchased (Simplify your answers.) inkjet printers, LCD monitors, and memory chips.

Answer 1

Solve Equations 109x+131y+83z=4921,x+y+z=49,-2y+z=0 using Elimination method

Solution:
Total Equations are 3

109x+131y+83z=4921→(1)

x+y+z=49→(2)

0x-2y+z=0→(3)


Select the equations (1) and (2), and eliminate the variable x.

109x+131y+83z=4921	×1→			109x	+	131y	+	83z	=	4921
		−
x+y+z=49	×109→			109x	+	109y	+	109z	=	5341
						22y	-	26z	=	-420	→(4)

Select the equations (3) and (4), and eliminate the variable z.

-2y+z=0	×26→				-	52y	+	26z	=	0
		+
22y-26z=-420	×1→					22y	-	26z	=	-420
					-	30y			=	-420	→(5)

Now use back substitution method
From (5)
-30y=-420

⇒y=-420-30=14

From (3)
-2y+z=0

⇒-2(14)+1z=0

⇒1z-28=0

⇒1z=0+28=28

From (2)
x+y+z=49

⇒1x+1(14)+1(28)=49

⇒1x+42=49

⇒1x=49-42=7

Solution using Elimination method.
x=7,y=14,z=28

The company purchased 7 inkjet printers, 14 LCD monitors ,and 28 memory chips