Need help setting up the problems. I\'ll try to shorten the question so if anyth

Question

Need help setting up the problems. I'll try to shorten the question so if anything doesn't makesense let me know. Pyro-Tech is upgrading computers by purchasing video cards,DVD drives, and additional memory chips. Total number of pieces of hardware purchased is 46. Cost of each video card is $109. Cost of each DVD drive is $129. Cost of each memory chip is $89. Total ammt of money spent on upgrades is $4774. They purchased twice as many memory chips as DVD drives. How many of each item was purchased? Need help setting up the problems. I'll try to shorten the question so if anything doesn't makesense let me know. Pyro-Tech is upgrading computers by purchasing video cards,DVD drives, and additional memory chips. Total number of pieces of hardware purchased is 46. Cost of each video card is $109. Cost of each DVD drive is $129. Cost of each memory chip is $89. Total ammt of money spent on upgrades is $4774. They purchased twice as many memory chips as DVD drives. How many of each item was purchased?

Explanation / Answer

Let viedo cards = y let dvd drives = x let memory cards = 2x ( twice as many memorychips as DVD drives) the first equation is.. 2x + x + y = 46 3x + y = 46 ---(a) ( How many they purchased.) the other equation is... 89(2x) + 129x + 109y = 4774 307x + 109y = 4774 -- (b) (How much they spent) In (a), y = 46 - 3x In (b)... 307x + 109y = 4774 307x + 109(46-3x) = 4774 307x + 5014 - 327x = 4774 -20x = 4774-5014 -20x = -240 and multiply -1 both sides. 20x = 240 x = 12 and.. that equation which is y = 46-3x.. y = 46 - 3x y = 46 - 3(12) y = 46 - 36 y = 10. so.. ANSWER IS.. video cards = y = 10 DVD drives = x = 12 memory chips = 2x = 24

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