GMAT Word Problems Explained — Hard drive, monitor, and printer for a certain desktop computer system cost

Question

The hard drive, monitor, and printer for a certain desktop computer system cost a total of 2,500USD. The cost of the printer and monitor together is equal to \frac{2}{3} of the cost of the hard drive. If the cost of the printer is 100USD more than the cost of the monitor, what is the cost of the printer?

Options:

A. $800USD$
B. $600USD$
C. $550USD$
D. $500USD$
E. $350USD$

word problemstranslationssimultaneous equations

Steps

Explanation	Calculations	Help
$We first create variables for each item to avoid ambiguity$	$H = cost of the hard drive M = cost of the monitor P = cost of the printer$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate the statement that all three costs sum to 2,500USD$	$H + M + P = 2500$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate that the combined cost of printer and monitor equals two-thirds of the hard drive cost$	$P + M = \frac{2}{3} H$	Theory & Tactics Method Card TRANS2-B Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We translate that the printer costs 100USD more than the monitor$	$P = M + 100$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We isolate the hard drive cost in terms of the monitor cost using algebra$	$2 M + 100 = \frac{2}{3} H H = 3 M + 150$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We substitute expressions for H and P into the total-cost equation$	$(3 M + 150) + M + (M + 100) = 2500$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We collect like terms and move constants to solve for M$	$5 M + 250 = 2500 5 M = 2250$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We divide both sides by 5 to find the monitor cost$	$M = 450$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We then find the printer cost by adding 100USD to the monitor cost$	$P = 450 + 100 = 550$	Theory & Tactics Method Card EQUA3-A Click to view full details

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Final Answer

550USD