Help?

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?

PsychoBaker
Jul 10, 2017

#1**0 **

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?

hectictar
Jul 10, 2017

#3**+2 **

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

CPhill
Jul 10, 2017