Hard question that I don’t know if you are able to solve

Question

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 were John and Nat given each?

Answer 1

J-50d= 2500

N-100d = 0

N= 100d

J-100D =1000

N-50D = 0

N=50D

100d =50D

2d =D

d doesn't equal D the number of days they're spending at the different daily rates

twice as many days in the 2nd situation

J-50D =2500

N-50D =1000

J-N=1500. John started with $1500 more than Nat

N+1500 -50d = 2500

N -50d = 1000

N-50D =0

N-100d =0

N=1000+50d =100d

50d = 1000

d = 20 days

D =40 days

J-50d=2500

J=2500+50(20)

J =2500+1000

J=$3500 to start

N=$2000 to start

N-50(40)=0

2000-50(40)=0

J-50(20) =2500

3500-1000=2500

John originally had $3500

Nat originally had $2000