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# Random Math Question

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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?

Jul 10, 2017

#1
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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?

Jul 10, 2017
#2
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Yup.

Jul 10, 2017
#3
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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

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