Solving Linear Equations to Determine Fruit Prices: A Real-World Problem Solved

Introduction

Mathematics is a powerful tool used in everyday life for various purposes. One such application is solving real-world problems through algebra. This article will walk you through solving a common math problem involving the cost of fruits using linear equations. We will use algebraic reasoning to find out how much a pear costs given the total cost and how much more a pear costs than an orange.

Problem Statement

The problem states: '8 pears and 2 oranges cost Rs 117. A pear costs Rs 4 more than an orange. What is the cost of a pear?' This can be translated into the following equations:

8x 2y 117, where x is the cost of a pear and y is the cost of an orange. x y 4

Solving the Equations

Method 1: Direct Substitution

Substituting the second equation into the first:

8(y   4)   2y  117

Expanding and simplifying:

8y   32   2y  117

10y   32  117

Subtracting 32 from both sides:

10y  85

Dividing both sides by 10:

y  8.5

Substituting y back into the second equation:

x  8.5   4  12.5

The cost of a pear is Rs 12.50.

Method 2: Simplification and Solving

We can represent the cost of an orange as y and the cost of a pear as x y 4. Therefore:

8(y   4)   2y  117

Expanding and simplifying:

8y   32   2y  117

Combining like terms:

10y   32  117

Subtracting 32 from both sides:

10y  85

Dividing both sides by 10:

y  8.5

The cost of a pear:

x  8.5   4  12.5

Conclusion

Using algebra, we can solve real-world problems involving costs and relationships between different items. In this case, we determined that a pear costs Rs 12.50. Understanding and applying algebraic concepts can greatly enhance our problem-solving skills in various fields, including finance, economics, and daily life.

Further Reading

For those interested in further exploring algebra and its applications, here are a few recommended resources:

Math is Fun: Algebra Khan Academy: Algebra Maths Got Served: Linear Equations