Solving Angelica’s Wallet Puzzle: A Comprehensive Guide

Welcome to this detailed guide on solving a classic money-related problem. The puzzle involves Angelica's wallet, where she has a specific combination of 20 peso and 50 peso bills totaling 1150 pesos, with an interesting condition that there are nine more 50 peso bills than 20 peso bills. This article will walk you through the step-by-step process of solving this problem, explaining the concept clearly and providing detailed calculations.

Understanding the Problem

The problem at hand can be summarized as follows: Angelica's wallet contains a mixture of 20 peso and 50 peso bills, with a total value of 1150 pesos. Moreover, there are nine more 50 peso bills than 20 peso bills. Our task is to identify how many 20 peso and 50 peso bills she has in her wallet.

Defining Variables

To solve this problem, we will define two variables:

x (x) represents the number of 20 peso bills. y (y) represents the number of 50 peso bills.

Setting Up the Equations

Based on the given information, we can set up the following equations:

The total amount of the bills is 1150 pesos:

2 50y 1150

There are nine more 50 peso bills than 20 peso bills:

y x 9

Solving the Equations

We can substitute the second equation into the first to solve for x:

Substituting y in the first equation:

2 50(x 9) 1150

Expanding the equation:

2 5 450 1150

Combining like terms:

7 450 1150

Subtracting 450 from both sides:

7 700

Dividing both sides by 70:

x 10

Now that we have x, we can find y:

y x 9 10 9 19

Therefore, Angelica's wallet contains 10 twenty peso bills and 19 fifty peso bills.

Verification

To verify the solution, we can substitute x and y back into the original equations:

Total value of the bills:

20(10) 50(19) 200 950 1150

The difference in the number of bills:

19 - 10 9

This confirms our solution is correct, as the values match the original problem statement.

Summary of Solution

Angelica’s wallet contains:

20 peso bills: 10 50 peso bills: 19

By setting up and solving the equations, we have successfully determined the exact number of each type of bill in Angelica’s wallet.

Conclusion

This problem demonstrates the application of algebraic equations to solve real-world problems. Understanding how to set up and solve such equations is a valuable skill in mathematics and in practical applications like managing finances.

For those who are interested in exploring similar problems and want to enhance their problem-solving skills, we recommend practicing with other money-related problems or algebraic puzzles. You can find many resources online that provide detailed solutions and explanations to help you master these concepts.