Let the amount of money John started with=M
Let the initial number of days =d
M - 50d =2500, M - 200d =1,000, solve for M, d
M=$3,000 original amount of money that John started with.
d=10 initial number of days.
Since Nan spent $100 per day initially, therefore she must have had:
10 x $100 =$1,000 to start with.
Since John spent $3,000 - $1,000 =$2,000 @ $100 per day, in the 2nd scenario, therefore it took him:
$2,000/$100=20 days to spend that money.