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A stack of 9,500 computer cards is to be read by an electronic card reader. A card reader that reads 200 cards/minute begins reading the cards but breaks down before completing the job. A new card reader, which reads 300 cards/minute, then completes the task. If it took a total of 40 minutes to read the stack of cards, how long did the first machine work before it broke down? (I tried to begin solving this by using the variable t for the length of time before machine 1 broke down but I could not derive a satisfactory equation from this. I am not a math major and this problem had me stumped. Could someone please show how this problem is solved? Thanks.)
ks write two equations: x + y = 40 and 200x +300y = 9500. Solve using substitution. 200x +300(40-x)=9500. Then x =25. The first machine worked 25 minutes at 200 cards per minute and the second worked for 15min at 300 cards/min for a total of 9500 cards.
Jun 2, 2018

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