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

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