Apple and Orange Cost Problem: A Comprehensive Explanation SEO Optimized Guide

Introduction to the Problem

Johnson bought 12 apples and 16 oranges with the apples being 2 cents less expensive than the oranges. The total cost of these fruits was $3.12. This article explores the different methods to solve this problem, providing a detailed step-by-step solution and including SEO-optimized keywords for better Google visibility.

Algebraic Equations Method

Let us assume the cost of an apple is (x) cents. Given that an apple is 2 cents less than an orange, the cost of an orange would be (x 0.02) cents.

Solution 1

The total cost can be represented by the equation:

[12x 16(x 0.02) 312]

Simplifying this equation:

[12x 16x 0.32 312]

[28x 0.32 312]

[28x 311.68]

[x frac{311.68}{28}]

[x 11.13]

This solution appears incorrect. Let's revisit the non-algebraic solution for a more intuitive understanding.

Solution 2

A simpler representation of the problem can be achieved by reframing the equation without decimals:

[12(x - 2) 16x 312]

[12x - 24 16x 312]

[28x - 24 312]

[28x 336]

[x frac{336}{28}]

[x 12]

Hence, the cost of each apple is $0.10 (10 cents) and the cost of each orange is $0.12 (12 cents).

Solution 3

Let (A) be the cost of an apple and (R) be the cost of an orange:

[12A 16R 312] (total cost in cents)

[A R - 2] (apples cost 2 cents less than oranges)

Substituting (R - 2) for (A):

[12(R - 2) 16R 312]

[12R - 24 16R 312]

[28R - 24 312]

[28R 336]

[R frac{336}{28}]

[R 12]

Since (A R - 2):

[A 12 - 2 10]

Thus, each apple costs 10 cents and each orange costs 12 cents.

Conclusion

This problem demonstrates the use of algebraic equations to solve real-world problems involving cost. Understanding and solving such equations efficiently is crucial in various fields, particularly in business and economics. By practicing these types of problems, one can enhance their problem-solving skills and improve their performance in mathematics.

SEO Tips for Google Familiarity

Ensure the content is rich and detailed, making it easily readable and engaging for readers. Utilize relevant keywords naturally throughout the text, such as cost problem and algebraic equations. Include subheadings and lists to make the content more digestible and improve readability. Regularly update similar content to show Google that the source is active and valuable."