Paul and Melissa bought some apple tarts. Paul's bill is $78 and Melissa's bill is $54. Paul bought 4 apple tarts more than Melissa. How many apple tarts did he buy? 

Let the number of apple tarts Melissa bought be $ x $. Since Paul bought 4 more apple tarts than Melissa, the number of apple tarts Paul bought is $ x + 4 $.

Now, we know the cost of Paul's tarts is $78 and Melissa's is $54. Let the price of each tart be $ p $.

From the given information, we can set up the following two equations:

1. Melissa's cost: 
\[
p \times x = 54
\]

2. Paul's cost:
\[
p \times (x + 4) = 78
\]

Now, we can solve these two equations to find $ x $.

### Step 1: Solve for $ p $ from Melissa's equation
\[
p = \frac{54}{x}
\]

### Step 2: Substitute $ p $ into Paul's equation
\[
\frac{54}{x} \times (x + 4) = 78
\]

Now, solve for $ x $:
\[
54(x + 4) = 78x
\]
\[
54x + 216 = 78x
\]
\[
216 = 24x
\]
\[
x = \frac{216}{24} = 9
\]

Thus, Melissa bought 9 apple tarts. Since Paul bought 4 more than Melissa, he bought:
\[
x + 4 = 9 + 4 = 13
\]

### Final Answer:
Paul bought 13 apple tarts.

Would you like a detailed explanation on any part of this? 

Here are some related questions for practice:
1. If each apple tart costs $6, what would be the total cost for both Paul and Melissa combined?
2. What would be the cost per tart if Paul had bought 6 more tarts than Melissa?
3. If Melissa had bought 3 fewer tarts, how would this change the total cost?
4. What is the difference between their total number of tarts?
5. How would the problem change if Melissa had bought twice as many tarts as she did?

**Tip**: When dealing with systems of equations, it's often helpful to express one variable in terms of the other to simplify solving!

Paul and Melissa bought some apple tarts. Paul's bill is $78 and Melissa's bill is $54. Paul bought 4 apple tarts more than Melissa. How many apple tarts did he buy?

Learn how to solve a system of equations in this real-world problem where Paul and Melissa buy apple tarts. Paul spent $78 and Melissa $54, with Paul buying 4 more tarts than Melissa. This example covers basic algebra and linear equations, suitable for Grades 6-8.

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