Question 1163541
john and nat were given some money. 
if john spends $50 and nat spends $100 each day, john would still have $2500 left
 while nat would have spent all her money. 
if john spends $100 and nat spends $50 each day, john would still have $1000 left
 while nat would have spent all her money.
How much money john and nat were given each?
:
In the first situation Nat spend all her money at $100 a day in x days
therefore
In the 2nd situation Nat must spend all money at $50 a day for 2x days
:
let j = amt of money that John had
let n = amt of money that Nate had
:
Johns two equations for x and 2x days
J - 50x = 2500
j - 100(2x) = 1000
----------------------subtraction eliminates j, find x
0 + 150x = 1500
x = 1500/150
x = 10 days for the first situation, then 20 days for the 2nd situation
:
Find j using the first situation: 
j - 50(10) = 2500
j = 2500 + 500
j = $3000 was John's original amt
then find n using the first situation
n - 100(10) = 0
n - 1000 = 0
n = $1000 was Nat's original amt