Formulate a system of equations to represent this situation, with f = the amount of money that Frank spent and r = the amount of money that Rachel spent. Frank and Rachel spent a total of $15.75. If Rachel spends twice as much money as Frank, how much money did they each spend?

We have:

 f: the amount of money that Frank spent.
 r = the amount of money that Rachel spent.
 
 The system of equations that represents this situation is:
 
 1) f+r=15.75
 2)r=2f
 
 Let's substitute r=2f into the equation 1):
 
 f+r=15.75
 f+2f=15.75
 3f=15.75
 f=15.75/3
 f=5.25

 Now, we must substitute f=5.25 into the second equation, as it shows below:
 
 r=2f
 r=2x5.25
 r=10.50
 
 
 How much money did they each spend? The answer is:
 
 Frank spent 5.25$ and Rachel spent 10.50$