Random Math Question

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?

Yup.

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)

And

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