Let's solve the problem step by step.

Step 1: Define the variables

Let:

• $x$ be the number of pumpkin pies sold.
• $y$ be the number of cherry pies sold.
• $z$ be the number of apple pies sold.

Step 2: Translate the word problem into equations

From the problem statement, we have the following relationships:

1. "The bakery sold 12 more apple pies than cherry pies": $z = y + 12$
2. "The bakery sold 5 more cherry pies than pumpkin pies": $y = x + 5$
3. The number of pumpkin pies sold is given as $x = 12$.

Step 3: Substitute and solve

First, substitute $x = 12$ into the second equation to find $y$: $y = 12 + 5 = 17$ Next, substitute $y = 17$ into the first equation to find $z$: $z = 17 + 12 = 29$

Step 4: Calculate the total number of pies sold

The total number of pies sold by the bakery is the sum of the apple pies, cherry pies, and pumpkin pies: $\text{Total pies} = z + y + x = 29 + 17 + 12 = 58$

Final Answer

The bakery sold 58 pies in total yesterday.

Would you like any further details or explanations? Here are some related questions you might find interesting:

1. How many slices of pumpkin pie were sold in total?
2. What percentage of the total pies sold were cherry pies?
3. If each apple pie was cut into 10 slices, how many total slices of apple pie were sold?
4. What if the bakery sold 10 more pumpkin pies? How would that affect the total number of pies sold?
5. Can we represent the relationship between the pies sold using a bar graph?

Tip: When solving word problems, it's helpful to first define variables and then carefully translate each sentence into an equation.