If the system of equation is correct, the solutions should be whole numbers.
The dollar bill does not belong in the box.
Practice makes perfect
From the exercise, we know that the box contains $200. If the total revenue from the 47 runners equals $201, the extra bill should likely be in the box. We can find out by examining the system of equations that describes this situation.
i+ f=47 5i+4f=200
What do these equations tell us?
The first equation tells us that the number of individual runners, i, and family runners, f, totaled 47 people.
The second equation tells us that the revenue from the individual runners, 5i, and family runners, 4f, is $200.
If this system describes the situation correctly, the solutions to this system of equations, i and f, have to be whole number values as fractions of people does not exist. Let's solve this system using the Substitution Method.
Great, the solutions for i and f are whole numbers so we can be sure the extra dollar is not from the charity run. However, Carter should not be shady dude and hand in the dollar bill to the police so it may find its rightful owner.
