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The problem reads as follows:

- Sara spends **$x** on pens, and each pen costs **$2.50**.
- She also spends **$(x - 14.50)** on pencils, and each pencil costs **$0.50**.
- The total number of pens and pencils is **19**.

We need to write and solve an equation for **x**.

### Step 1: Define Variables
Let:
- **n₁** be the number of pens.
- **n₂** be the number of pencils.

From the information given:
- For pens: $ \text{Number of pens} = \frac{x}{2.50} $
- For pencils: $ \text{Number of pencils} = \frac{x - 14.50}{0.50} $

The total number of pens and pencils is 19, so we have the equation:
\[
\frac{x}{2.50} + \frac{x - 14.50}{0.50} = 19
\]

### Step 2: Solve the Equation

1. Simplify each fraction:
   \[
   \frac{x}{2.50} = \frac{x}{\frac{5}{2}} = \frac{2x}{5}
   \]
   \[
   \frac{x - 14.50}{0.50} = \frac{x - 14.50}{\frac{1}{2}} = 2(x - 14.50)
   \]

2. Substituting these into the equation:
   \[
   \frac{2x}{5} + 2(x - 14.50) = 19
   \]

3. Expand the second term:
   \[
   \frac{2x}{5} + 2x - 29 = 19
   \]

4. Combine like terms:
   \[
   \frac{2x}{5} + 2x = 48
   \]

5. Multiply the entire equation by 5 to eliminate the fraction:
   \[
   2x + 10x = 240
   \]

6. Combine terms:
   \[
   12x = 240
   \]

7. Solve for **x**:
   \[
   x = \frac{240}{12} = 20
   \]

### Final Answer:
The value of **x** is **20**.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How many pens did Sara buy?
2. How many pencils did Sara buy?
3. If Sara had spent $30 on pens, how many total items could she have bought?
4. What would be the equation if the cost per pencil was $0.75 instead?
5. How much more would Sara have spent if she had bought 25 items instead of 19?

**Tip:** When dealing with cost per item and total expenditures, always set up the equations carefully to match the number of items purchased.

Sara spends $x on pens which cost $2.50 each. She also spends $(x - 14.50) on pencils which cost $0.50 each. The total number of pens and pencils is 19. Write down and solve an equation in x.

Learn how to solve an algebraic equation where Sara spends $x on pens and pencils, and the total number of items is 19. This problem covers key algebra concepts related to linear equations and word problems, suitable for students in Grades 6-8.

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