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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
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3+0 Answers

 #1
avatar+4060 
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
 #2
avatar+178 
0

Yup.

PsychoBaker  Jul 10, 2017
 #3
avatar+75017 
+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

 

 

 

cool cool cool

CPhill  Jul 10, 2017
edited by CPhill  Jul 10, 2017
edited by CPhill  Jul 10, 2017

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