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Question 332774: I own a company that sells high-end computers; I made 2 orders from a vendor: the first one was for 1300 desktops and 400 laptops totaling $48,700. The second order was for 600 desktops and 200 laptops totaling $23,200. The receipts were not itemized. What is the cost of one desktop and one laptop?
I need to be able to show the work.
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! let D=cost of desktop
let L=cost of laptop
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you have these two unknowns, so you need two independet equations to solve
(always need as many equations as there are unknowns!!)
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you are given
order #1: 1300*D + 400*L=48700
order #2: 600*D + 200*L=23200
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simplify (always simply if can, to save you effort later on)
divide first equation by 100
13*D + 4*L=487
divide second equation by 200
3*D + L=116
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now you can either solve via by elimination or substitution (among many other methods)
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try elimination
13*D +4*L=487
3*D + L =116 (multiply this equation by -4)
-12*D-4*L = -464
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add the first and modified 3rd equation, to eliminate the L variable
D=487-464=23
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since D=23, go upstream and subtitute this D=23 into one of the equation to solve for L
13*D +4*L=487
3*D + L =116 i'll choose this one
3*(23) + L =116
L=116-3*(23) =47
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so, D=23 and L=47
check with the original equations to make sure no mistake was made
order #1: 1300*D + 400*L=48700 check 1300*23+400*47
order #2: 600*D + 200*L=23200 check 600*23+200*47
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