q9 edited

problems/fa24-midterm/q09.md

@@ -5,7 +5,7 @@ fun-sized. Suppose we have an additional DataFrame, `trick`, which is
 indexed by `"candy"` and has one column, `"price"`, containing the cost
 in dollars of a **single piece** of fun-sized candy, as a `float`.
 
-Suppose that:
+Suppose that\:
 
 -   `treat` has 200 rows total, and includes 15 distinct types of
     candies.
@@ -14,7 +14,7 @@ Suppose that:
     `treat`, plus 10 additional rows that correspond to candies not
     represented in `treat`.
 
-Consider the following line of code:
+Consider the following line of code\:
 
     trick_or_treat = trick.merge(treat, left_index = True, right_on = "candy")
 
@@ -30,9 +30,16 @@ How many rows does `trick_or_treat` have?
 
 # BEGIN SOLUTION
 
-**Answer**: 200
+**Answer**\: 200
 
-<average>44</average>
+We are told that `trick` has 25 rows\: 15 from candies that are in `treat` and 10 additional candies. 
+This means that each candy in `trick` appears exactly once because 15+10= 25. In addition, a general
+property when merging dataframes is that the number of rows for one shared value between the dataframes is 
+the product of the number of occurences in either dataframe. For example, if Twix occurs 5 times
+in `treat`, the number of times it occurs in `trick_or_treat` is 5 * 1 = 5 (it occurs once in `trick`). 
+Using this logic, we can determine how many rows are in `trick_or_treat`. Since each number of candies is multipled by one and they sum up to 200, the number of rows will be 200. 
+
+<average>39</average>
 
 # END SOLUTION