Franklin sold water bottles in two sizes, large ($2.50 each) and regular ($1 each). He sold 113 bottles altogether and collected $221 dollars. How many bottles of each type did he sell?

Let's make a system of equations.

1 large bottle = l

1 regular bottle = r

l + r = 113

221 = 2.5l + r

Isolate r in the first equation and substitute it into the second equation:

l + r = 113

r = 113 - l

---

221 = 2.5l + 113 - l

221 = 1.5l + 113

108 = 1.5l

72 = l

Now, substitute that back into the first equation:

l + r = 113

72 + r = 113

r = 41

Finally, check your work by substituting back into both equations:

72 + 41 = 113 - - > 113 = 113 < - - True

221 = 2.5 (72) + 41 - - > 221 = 180 + 41 <--True

Answer:

Franklin sold 72 large bottle of water and 41 regular-sized bottles of water.