The hard drive, monitor, and printer for a certain desktop computer system cost a total of...

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 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?

GMAT Panda · Accepted Answer

550USD 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 We translate the statement that all three costs sum to 2,500USD H + M + P = 2500 We translate that the combined cost of printer and monitor equals two-thirds of the hard drive cost P + M = 2/3H We translate that the printer costs 100USD more than the monitor P = M + 100 We isolate the hard drive cost in terms of the monitor cost using algebra 2M + 100 = 2/3H H = 3M + 150 We substitute expressions for H and P into the total-cost equation (3M + 150) + M + (M + 100) = 2500 We collect like terms and move constants to solve for M 5M + 250 = 2500 5M = 2250 We divide both sides by 5 to find the monitor cost M = 450 We then find the printer cost by adding 100USD to the monitor cost P = 450 + 100 = 550

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

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