Exercise #1: Jonathan has nine bills in his wallet that are all either five-dollar bills or ten-dollar bills.
(a) Fill out the following table to see the (b) If f represents the number of $5 bills and t dependence of the two variables and how they represents the number of $10 bills, then what then determine how much money Jonathan has. does the following expression calculate? Explain.
Number Number
of fives, f of tens, t Amount of Money, $
0
1
2
3
b) If f represents the number of $5 bills and t represents the number of $10 bills, then what does the following expression calculate? Explain. 5 f + 10 t

(c) If Jonathan has a total of $55, set up a system of equations involving f and t that could be used to determine how many of each bill he has. Solve the system. Remember that he has 9 total bills.

(d) Let’s say that we were told that Jonathan had seven bills that were all 5’s and 20’s and we were also told that he had a total of $120. Set up and solve a system to help evaluate whether we could have been told true information.

Exercise #2: Samantha went to a concession stand and bought three pretzels and four sodas and paid a total of $11.25 for them. Raza went to the same stand and bought five pretzels and two sodas and paid a total of $8.25.

(a) Could pretzels have cost $1.75 each and sodas $1.50 each? How can you evaluate based on the information given?

(c) Solve the system of equations using the elimination method.

(b) Letting x equal the unit cost of a pretzel and letting y equal the unit cost of a soda, write a system of equations that models the information given.

(d) If Leah went to the same concession stand and bought two sodas, how many pretzels would she need to buy so that she spent the same amount on both?

Exercise #3: A rectangle has a perimeter of 204 feet. It’s length is six feet longer than twice its width. If L stands for the length of the rectangle and W stands for its width, write a system of equations that models the information given in this problem and solve it to find the length and width of this rectangle.