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Both David and Eric had an equal amount of money at first. Every month, David spent $850 and Eric spent $912. After a few months, David was left with $1550 while Eric had 4/5 of the money David had left. How much did Eric have at first?

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2 answers
  1. 4/5 of $1550 = $1240
    If they both started with $x and spent for m months, then
    x - 912m = 1240
    x - 850m = 1550
    Subtract to find that they spent money for 5 months
    so Eric started with 1240 + 5*912 = $5800

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  2. amount of money each had at first --- x
    after n months:
    David had x - 850n
    Eric had x - 912n

    x - 850n = 1550
    x = 1550 + 850n , #1

    x - 912n = (4/5)1550 , #2
    5x - 4560n = 6200
    5x = 6200 + 4560n
    x = 1240 + 912n

    912n + 1240 = 1550 + 850n
    62n = 310
    n = 5
    then x = 1240 + 912(5) = 5800
    Since it said that they had equal amounts , Eric had 5800

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