Problem 89 - Elementary Algebra

Question

Victoria bought two pounds of Gala apples at \(\$ 1.79\) per pound and three pounds of Fuji apples at \(\$ 0.99\) per pound. How much did she spend for the apples?

Step-by-Step Solution

Answer

She spent $6.55 for the apples.

Step 1: Calculate Cost of Gala Apples

Victoria bought two pounds of Gala apples at a rate of \(\$ 1.79\) per pound. To find the total cost for the Gala apples, multiply the cost per pound by the number of pounds: \(2 \times 1.79 = 3.58\).

Step 2: Calculate Cost of Fuji Apples

Victoria bought three pounds of Fuji apples at a rate of \(\$ 0.99\) per pound. To find the total cost for the Fuji apples, multiply the cost per pound by the number of pounds: \(3 \times 0.99 = 2.97\).

Step 3: Add Total Costs

To find the total amount spent on all apples, add the total cost of Gala apples and the total cost of Fuji apples: \(3.58 + 2.97 = 6.55\).

Key Concepts

Multiplication

Multiplication is an essential mathematical operation used when you need to find the total number of items when they come in identical groups. For instance, if you're purchasing items priced per unit, such as apples per pound, multiplication helps calculate the total cost for multiple units. In the exercise, Victoria bought two pounds of Gala apples, each priced at $1.79. Instead of adding the price per pound to itself, we use multiplication to simplify the calculation:

• The formula becomes: Number of pounds × Cost per pound = Total cost.
• For Gala apples, it's: \(2 \times 1.79 = 3.58\).

This calculation tells you how much she spent on Gala apples. Multiplication thus saves time and reduces errors compared to repeatedly adding the same number.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. It is often used after individual multiplications to combine costs, quantities, or other items.In Victoria's exercise, after separately calculating the costs for each type of apple, you need to find the total amount she spent in all. This is where addition comes into play:

• First, calculate the individual costs: Gala apples as \(3.58\) and Fuji apples as \(2.97\).
• Next, add these values together: \(3.58 + 2.97 = 6.55\).

Addition effectively combines these separate amounts into one total, providing the answer to the question of the total cost spent on apples.

Cost Calculation

Cost calculation is the comprehensive process of determining the total expense incurred when purchasing items. In solving arithmetic word problems, it's crucial to distinguish between repeated costs and one-time sums. Here's how cost calculation is structured deductively in the exercise:

• Begin with determining the individual costs for each type of apple using multiplication.
• Gala apples: Number of pounds \(2\) times the cost per pound \(1.79\) equals \(3.58\).
• Fuji apples: Number of pounds \(3\) times the cost per pound \(0.99\) equals \(2.97\).
• Combine the separate expenses using addition: \(3.58 + 2.97\), resulting in \(6.55\).

This calculated total represents the entire cost Victoria incurred purchasing the apples, providing a clear and methodical way of tackling arithmetic word problems involving cost.