How to Determine the Cost Ratio of Bananas to Apples Using Equations

Mathematics often intertwines with our daily experiences, such as shopping in a grocery store. For instance, determining the cost ratio of bananas to apples based on a given equation is a straightforward yet engaging problem. This article aims to elucidate the method to solve this problem, guiding you through the process of finding the cost ratio of one banana to one apple using algebraic equations.

Problem Statement

The problem is stated as follows: 'Five bananas and four apples cost as much as three bananas and seven apples.' We need to determine the cost ratio of one banana to one apple.

Solution

To solve this problem, we will use algebraic equations. Let's denote the cost of one banana as x and the cost of one apple as y.

Step 1: Setting Up the Equation

According to the problem, we have the following equation:

5x 4y 3x 7y

Step 2: Simplifying the Equation

We need to isolate the variables on one side of the equation. Let's subtract 3x and 4y from both sides:

5x - 3x 7y - 4y

Simplifying this, we get:

2x 3y

Step 3: Finding the Ratio

Now, we need to express this in terms of the ratio of the cost of one banana to the cost of one apple:

x / y 3 / 2

Therefore, the ratio of the cost of one banana to the cost of one apple is 3:2.

Conclusion

In summary, we have successfully found the cost ratio of one banana to one apple given the initial problem statement. This problem illustrates the application of simple algebraic equations in solving practical problems, such as determining the cost of fruits in a grocery store.

Related Problems and Further Exploration

There are several similar problems that one can work on to further explore the concepts of cost ratios and algebraic equations:

Determining the cost ratio of two different items based on a given equation. Solving systems of linear equations to find multiple cost ratios. Exploring real-world applications of these mathematical concepts in everyday scenarios.

Understanding and solving these problems will not only enhance your algebraic skills but also help you in making informed decisions in your day-to-day life.