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? solution
Found 3 solutions by jim_thompson5910, ankor@dixie-net.com, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Let's say that 10 days pass by.
If Nat spents $100 a day, and runs out of money at the end of 10 days, then she has 100*10 = 1000 dollars total.
If she spends 50 dollars a day, then 50*10 = 500 is the amount she spends over the same duration of time. She doesn't spend all her money here. It seems like your teacher made a typo somewhere.
There is no way Nat spends all her money if she spends half as much and the duration of time is the same. I would ask your teacher about this.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! 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
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
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?
~~~~~~~~~~~~~
Let J be the amount John had initially and let x be the number of days in the 1-st scenario.
Let N be the amount Nat had initially and let y be the number of days in the 2-nd scenario.
For the first scenario, we have these two equations
J = 50x + 2500, (1)
N = 100x. (2)
For the second scenario, we have these two equations
J = 100y + 1000, (3)
N = 50y. (4)
In all, we have 4 equations in 4 unknown J, N, x and y, so we have a chance to solve it.
From eq(2), express x =  and substitute it into eq(1). You will have
J = 50*(N/100) + 2500, or J = (1/2)*N + 2500, or 2J - N = 5000 (5)
From eq(4), express y =  and substitute it into eq(3). You will have
J = 100*(N/50) + 1000, or J = 2N + 1000, or J -2N = 1000 (6)
Thus, we reduced the problem to two equations in 2 unknowns
2J - N = 5000 (5)
J - 2N = 1000 (6)
From eq(6), express J = 2N + 1000 and substitute it into eq(5). You will get
2*(2N + 1000) - N = 5000,
which implies
4N + 2000 - N = 5000
3N = 5000 - 2000 = 3000
N = 3000/3 = 1000.
Then from eq(5)
2J = 5000 + 1000 = 6000
J = 6000/2 = 3000.
ANSWER. John had 3000; Nat had 1000.
Solved.
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