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$