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Chapter 4: Problem 27

Set up an equation and solve each problem. (Objectives 2 and 3) Suppose that Jack bought a \(\$ 32\) putter on sale for \(35 \%\) off. How much did he pay for the putter?

Short Answer

Expert verified
Jack paid $20.80 for the putter.

Step by step solution

01

Determine the Amount of Discount

The first step is to find the discount amount. Since Jack received a 35% discount on a \(32 putter, we can calculate the discount amount using the formula for percentage: \[ \text{Discount Amount} = \text{Original Price} \times \frac{\text{Discount Percentage}}{100} \]Plug the values:\[ \text{Discount Amount} = 32 \times \frac{35}{100} = 32 \times 0.35 = 11.2 \] So, the discount amount is \)11.20.
02

Calculate the Final Price After Discount

To find out how much Jack paid, subtract the discount amount from the original price of the putter: \[ \text{Final Price} = \text{Original Price} - \text{Discount Amount} \]Plug the values:\[ \text{Final Price} = 32 - 11.2 = 20.8 \]Therefore, Jack paid $20.80 for the putter.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentage Discount
In this problem, the concept of percentage discount is crucial. A percentage discount involves reducing the original price of an item by a certain percentage. The discount is calculated as a fraction of 100 percent. Here, Jack receives a 35% discount on a putter priced at $32. To compute the discount, convert the percentage to a decimal. This is done by dividing the percentage by 100. For example, 35% becomes 0.35. Then, multiply the decimal by the original price to determine the discount amount. In Jack's case:
  • Convert 35% to decimal: 35/100 = 0.35
  • Calculate discount amount: 32 脳 0.35 = $11.20
This result tells us that Jack's discount on the putter is $11.20.
Effective Equation Setup
Setting up an equation correctly is a fundamental step in solving mathematical problems like these. When dealing with a percentage discount problem, the goal is usually to find the final amount paid after applying the discount.The key equation components here are:
  • Original Price of the item: Let's denote it by \( P \), which is $32 in this case.
  • Discount Percentage: Represented as \( d \), which is 35% or 0.35 in decimal form.
  • Discount Amount: Denoted by the equation \( D = P \times d \).
  • Final Price: This is what Jack actually pays, represented by \( F = P - D \).
Plugging in the values given in this scenario allows us to find the value of \( D \) first, and then subtract it from \( P \) to get \( F \). This is a clear approach that organizes your method and ensures accuracy.
Guided Problem-Solving Steps
After understanding the concepts of percentage discount and equation setup, it's time to apply them through structured problem-solving steps. Solving such algebra problems efficiently involves breaking down each task systematically.
Step 1: **Determine the Discount Amount**
  • Identify the original price: \(32.
  • Convert the percentage discount into a decimal: 35% becomes 0.35.
  • Use the formula \( D = P \times d \) to find the discount amount: \( 32 \times 0.35 = 11.2 \).

Step 2: **Calculate the Final Price After Discount**
  • Subtract the discount amount from the original price: \( F = 32 - 11.2 = 20.8 \).
  • So, Jack pays \)20.80 for the putter.
These steps break down the task into manageable parts, ensuring a clear pathway from question to answer. Following such organized steps helps avoid errors and builds confidence in problem-solving skills.

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