https://file.aiquickdraw.com/mathbot/file/1729435007402uggoowb5.jpg

Let's break down the problem in steps.

### a) Form an equation:
Let:
- $ x $ represent the number of paint sets.
- $ y $ represent the number of sketchpads.

From the problem, we know:
1. Each paint set costs $20.
2. Each sketchpad costs $5.
3. Sophia bought a total of 10 items.
4. The total cost was $150.

Thus, we can form two equations:
- Equation 1: The total number of items is 10, so:
  \[
  x + y = 10
  \]
- Equation 2: The total cost is $150, where paint sets cost $20 each and sketchpads cost $5 each:
  \[
  20x + 5y = 150
  \]

### b) Solve the equation to find the number of sketchpads:
We will solve this system of equations using substitution or elimination.

#### Step 1: Solve for one variable in Equation 1
From the first equation:
\[
x + y = 10 \quad \text{or} \quad x = 10 - y
\]

#### Step 2: Substitute into Equation 2
Substitute $ x = 10 - y $ into the second equation:
\[
20(10 - y) + 5y = 150
\]
Simplify:
\[
200 - 20y + 5y = 150
\]
\[
200 - 15y = 150
\]
Subtract 200 from both sides:
\[
-15y = -50
\]
Solve for $ y $:
\[
y = \frac{-50}{-15} = \frac{50}{15} = \frac{10}{3} \approx 3.33
\]

Since the number of items must be an integer, it's likely there's a small adjustment or rounding needed in the problem details, but this equation gives us an approximate solution.

Sophia is shopping for art supplies. She buys paint sets and sketchpads. Each paint set costs $20, and each sketchpad costs $5. If she bought a total of 10 items and spent $150, how many sketchpads did she buy?

Learn how to solve a linear equation involving the total cost and quantity of items. In this problem, Sophia buys paint sets and sketchpads with a total cost of $150 for 10 items. Understand how to form and solve equations for cost and quantity. Ideal for Grades 7-9.

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