understanding proportions in shopping

Understanding Proportions in Shopping

Introduction to Proportions

  • Proportions are equations that express the equality of two ratios. They are commonly used in various real-life situations, including shopping.

Example of Using Proportions in a Shopping Scenario

  • Problem Statement: Determine the cost of six cans of soup if four cans cost $2.

Setup of the Proportion

  • The relationship can be expressed as a proportion:

    • 42=6x\frac{4}{2} = \frac{6}{x}

    • Where:

    • 4 represents the number of cans of soup (known quantity).

    • 2 represents the cost of the four cans in dollars (known quantity).

    • 6 represents the number of cans of soup for which we want to find the cost (unknown quantity).

    • x represents the unknown cost of the six cans.

Steps to Solve the Proportion

  1. Multiply to find the value of x:

    • Multiply both sides of the proportion to eliminate the fraction:

    • 6×2=126 \times 2 = 12

    • This represents the total cost for six cans.

  2. Divide to find the unknown variable x:

    • Now, divide the total cost by the number of cans on the left side to find the single can cost:

    • 124=3\frac{12}{4} = 3

    • Therefore, the cost for six cans of soup, represented by x, is $3.

Conclusion

  • Final Answer: Six cans of soup cost $3. This demonstrates a practical application of solving a proportion which is a valuable skill during shopping, especially when dealing with discounts or bulk pricing comparisons.