Worksheet for calculating sale prices and discounts using percent proportions.

It seems like the task involves solving a problem related to calculating SALE PRICE and DISCOUNT using percentages. The image you uploaded outlines two methods for solving such problems: Method 1 (Thinking Before) and Method 2 (Setting Up the Proportion). Below, I will explain both methods in detail and solve a sample problem step by step.

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Problem Statement:

The problem involves finding the sale price of a $500 grandfather clock after a 30% discount is applied.

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Method 1: Thinking Before

This method involves breaking down the problem into logical steps before setting up any equations.

#### Steps:
1. Understand the Discount Percentage:
- The original price of the grandfather clock is $500.
- A 30% discount means 30% of the original price is taken off.

2. Calculate the Discount Amount:
- Discount amount = 30% of $500
- Discount amount = \( \frac{30}{100} \times 500 = 0.30 \times 500 = 150 \)

3. Calculate the Sale Price:
- Sale price = Original price - Discount amount
- Sale price = \( 500 - 150 = 350 \)

#### Final Answer for Method 1:
The sale price is $350.

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Method 2: Setting Up the Proportion

This method involves setting up a proportion based on the relationship between the original price, the discount percentage, and the sale price.

#### Steps:
1. Set Up the Proportion:
- Let the sale price be \( x \).
- Since a 30% discount is applied, the customer pays 70% of the original price (because \( 100\% - 30\% = 70\% \)).
- The proportion can be set up as:
\[
\frac{\text{Sale Price}}{\text{Original Price}} = \frac{70}{100}
\]
or
\[
\frac{x}{500} = \frac{70}{100}
\]

2. Solve the Proportion:
- Cross-multiply to solve for \( x \):
\[
x \cdot 100 = 500 \cdot 70
\]
\[
100x = 35000
\]
\[
x = \frac{35000}{100} = 350
\]

#### Final Answer for Method 2:
The sale price is $350.

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Comparison of Methods:

- Method 1 is more intuitive and involves direct calculations.
- Method 2 uses proportions, which can be helpful for more complex problems where relationships need to be explicitly defined.

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Final Answer:

Using either method, the sale price of the grandfather clock after a 30% discount is:

\[
\boxed{350}
\]