Problem 51 - Elementary Algebra

Question

Mary purchased 14 bottles of water at \(\$ 0.75\) per bottle, 4 pounds of assorted candy at \(\$ 3.50\) per pound, and 16 packages of microwave popcorn costing \(\$ 0.50\) each for her party. What was her total bill?

Step-by-Step Solution

Answer

Mary's total bill was \( \$32.50 \).

Step 1: Calculate the Cost of the Bottled Water

Mary bought 14 bottles of water, each costing \( \\(0.75 \). To find the total cost for the water, multiply the number of bottles by the cost per bottle: \( 14 \times 0.75 = \\)10.50 \).

Step 2: Calculate the Cost of the Candy

Mary bought 4 pounds of candy priced at \( \\(3.50 \) per pound. To find the total cost for the candy, multiply the number of pounds by the cost per pound: \( 4 \times 3.50 = \\)14.00 \).

Step 3: Calculate the Cost of the Microwave Popcorn

Mary bought 16 packages of microwave popcorn at \( \\(0.50 \) per package. Multiply the number of packages by the cost per package to get the total cost: \( 16 \times 0.50 = \\)8.00 \).

Step 4: Add All the Costs Together

Add the costs for the bottled water, candy, and microwave popcorn to find the total bill: \( \\(10.50 + \\)14.00 + \\(8.00 = \\)32.50 \).

Key Concepts

Understanding Cost Calculation

Calculating costs involves simply multiplying the number of items by their price. For instance, if you purchase multiple bottles of water or packages of candy, you need to determine the total expense by using this multiplication principle.
Mary's purchases involved three different products: bottled water, candy, and microwave popcorn. Each product has its unique price tag.

• Bottled Water: You multiply the number of bottles by the price per bottle. So, 14 bottles at \(0.75 each gives us: \(14 \times 0.75 = 10.50\)
• Candy: Use the same principle, 4 pounds at \)3.50 per pound: \(4 \times 3.50 = 14.00\)
• Microwave Popcorn: Multiply 16 packages by $0.50 each: \(16 \times 0.50 = 8.00\)

This step-by-step approach ensures you don't miss any product costs, providing accurate expense tracking.

Effective Problem-Solving Strategies

When solving a problem like Mary's total bill, the goal is to break down the task into smaller, manageable parts. This problem-solving method makes complex questions easier to digest.
Identify what each part of the problem requires you to do and tackle them one at a time.

• Breakdown tasks: Separate the items purchased and tackle each one. This provides a clear path.
• Write down each step: Visualization through writing helps you to see what's needed.
• Check your math: Before finalizing, always check to ensure each part was calculated correctly.

By following such methods, you build a foundation that makes you confident in tackling similar algebraic cost calculations in the future.

Mastering Arithmetic Operations

Arithmetic operations are the backbone of solving cost-related problems. Understanding basic operations such as addition, multiplication, and division is key to finding solutions.
In Mary's example, multiplication was used to calculate the total product cost, while addition was used to find the total bill.

• Multiplication: Used to calculate total costs, multiplying price by quantity (e.g., \(14 \times 0.75\) for water).
• Addition: Summing up all calculated costs to find the total bill (e.g., \(10.50 + 14.00 + 8.00\)).

By consistently practicing arithmetic operations, math problems become more approachable and less daunting. Develop these skills to become a more effective problem solver.