Question

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?

Answer 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

Answer 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