James and Jamie were given some money.
If James spends $50 and Jamie spends $100 each day,
James would still have $2500 and Jamie would've have spent all her money.
if James spends $100 and Jamie spends $50 each day,
James would still have $1000 while Jamie would've spent all her money.
How much were James and Jamie given each?
If Jamie spends $100 each day, she would have spent all her money.
If Jamie spends $50 each day, she would have spent all her money.
Are these supposed to be about the same number of days each time?
It can't be the same number of days....because Jamie exhausts all her money by spending $100 a day and then exhausts all her money by spending $50 per day......the second scenario must take twice as long as the first
So....let m be the amount of money they started with in total....and let x be the number of days in the first scenario and 2x be the number of days in the second scenario....so we have that
m - 50x - 100x = 2500 → m - 150x = 2500 (1)
m - 100(2x) - 50(2x) = 1000 → m - 300x = 1000 (2)
Subtract (2) from (1)
150x = 1500 → x = 10
Plugging this back into (1) we have that
m - 150(10) = 2500
m - 1500 = 2500
m = 4000 this is what they started with combined
And Jamie started with 100 (10) = $1000
So James started with $3000
Check...in the first scenario of ten days.....James spends 50 (10) = $500 and has $2500 left....while Jamie spends 100 (10) = $1000 and has nothing left
In the second scenario of twenty days....James spends 100 (2*10) = $2000 and has $1000 left while Jamie spends 50 ( 2 * 10) = 50 * 20 = $1000 and has nothing left