Timothy spent half his money on 24 files and the rest on 17 storybooks. Each storybook costs $3.15 more than each file. How much did he spend altogether?

Let's solve the problem step by step.

### Step 1: Define Variables
- Let the cost of each file be $ x $.
- Therefore, the cost of each storybook is $ x + 3.15 $.

### Step 2: Write Equations
- Timothy spent half of his money on 24 files:  
  $ 24x $ is the amount spent on files.
- He spent the other half on 17 storybooks:  
  $ 17(x + 3.15) $ is the amount spent on storybooks.

Since both halves are equal:
\[
24x = 17(x + 3.15)
\]

### Step 3: Solve for $ x $
First, expand the equation:
\[
24x = 17x + 53.55
\]

Now, subtract $ 17x $ from both sides:
\[
7x = 53.55
\]

Next, divide both sides by 7:
\[
x = 7.65
\]

### Step 4: Calculate the Total Cost
- The cost of one file is $ x = 7.65 $.
- The cost of one storybook is $ x + 3.15 = 7.65 + 3.15 = 10.80 $.

Now, calculate the total amount Timothy spent:
- Amount spent on files: $ 24 \times 7.65 = 183.60 $
- Amount spent on storybooks: $ 17 \times 10.80 = 183.60 $

### Step 5: Find the Total Amount Spent
Since Timothy spent an equal amount on both files and storybooks:
\[
\text{Total amount spent} = 183.60 + 183.60 = 367.20
\]

**Timothy spent a total of $367.20.**

Would you like further details or have any questions?

Here are 5 related questions to expand on this problem:
1. If Timothy had spent the same amount on 20 files and 15 storybooks, what would have been the total cost?
2. What if the price of the storybook was $5 more than the file? How would that change the total amount spent?
3. How much would Timothy have spent if each file cost $8 and each storybook $11?
4. If Timothy had bought 30 files instead of 24, what would have been the new total amount spent?
5. What would be the cost per item if the total amount spent remained the same, but the number of files and storybooks were swapped?

**Tip:** When dealing with cost problems, setting up clear equations with variables helps break down and solve the problem efficiently.

Explore how Timothy spends his money on 24 files and 17 storybooks, with each storybook costing $3.15 more than each file. Learn the step-by-step solution to find out the total amount Timothy spent. Suitable for Grades 6-8.

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