Solving a Word Problem Using Algebra

Introduction

Algebra is a powerful tool in solving real-life problems, such as financial ones. This article will guide you through solving a word problem related to the purchase of cannolis and pies. Understanding these types of problems can be greatly beneficial for SEO, especially when you're dealing with content related to math, finance, or educational resources.

The Problem

Lakan bought a total of 40 cannolis and pies. Each cannoli costs $2.75, and each pie costs $5.20. The pies cost $9.25 more than the cannoli. How many of each did Lakan buy?

Solution 1: Substitution Method

Let's start with a simple method that involves substitution:

Let c be the number of cannolis and p be the number of pies. The total number of items is:

c p 40

The cost of the cannolis is 2.75c, and the cost of the pies is 5.20p. The cost of the pies is $9.25 more than the cannolis:

5.20p 2.75c 9.25

Since c 40 - p, we can substitute this into the second equation:

5.20p 2.75(40 - p) 9.25

Solving for p gives:

5.20p 110 - 2.75p 9.25

5.20p 2.75p 119.25

7.95p 119.25

p 15

c 40 - 15 25

Solution 2: Equation Method

In this method, we set up and solve a system of equations:

c p 40

5.20p 2.75c 9.25

We start with the substitution of c 40 - p into the second equation:

5.20p 2.75(40 - p) 9.25

Multiplying and combining like terms gives:

5.20p 110 - 2.75p 9.25

5.20p 2.75p 119.25

7.95p 119.25

p 15

c 40 - 15 25

Solution 3: Direct Equation Method

This method uses a more straightforward equation setup:

Let X be the number of cannolis, so the number of pies is 40 - X.

The difference in cost is given as:

(40 - X) * 5.20 - X * 2.75 9.25

Expanding and solving for X gives:

208 - 5.2 - 2.75X 9.25

-7.95X -198.75

X 25

40 - X 15

Conclusion

Your calculations and methods will be cleaner and more efficient if you choose one approach over the others. Practice using these methods to solve similar problems for better performance in SEO and general problem-solving.

Keywords

Word problem, algebraic equation, cost calculation, price difference, Google SEO