SOLUTION: 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

Algebra.Com
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(52787)   (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.



RELATED QUESTIONS

Stuart and Dave each had some money. If Stuart spends 3 times the amount Dave spends each (answered by ikleyn)
How long would it take john to spend one million dollars if he spends $ 1000 each... (answered by TimothyLamb,ewatrrr)
John have 300 pounds and peter have 1860 pounds.if john saves 50 pounds a day and peter... (answered by checkley79)
From his salary,john spends 15%on rents,20%on transport and 50% on groceries. If he saves (answered by ikleyn)
Hi Alex and Blinman have some money. If Alex spends 40 dollars and Belinda spends 80... (answered by ikleyn,Edwin McCravy)
John Receives a $35000 salary for working as an agent. if John spends 80% of his salary... (answered by Cromlix)
John spends $ 8.40 in buying 100 postage stamps. If x of them are 7 cents stamps & y are... (answered by rfer)
John spent 1/2 of his money in the supermarket and 1/3 in the store, what fraction of the (answered by MathLover1)
Josephine and Kelly collected some stickers. If Josephine and Kelly gave away 50 and 25... (answered by richwmiller)