Solving Coin Conversion Problems: A Step-by-Step Guide
When dealing with real-world money-related problems, it often involves converting between different coins or currencies. This article will guide you through solving a practical problem involving coin conversion using basic algebra. Our focus will be on a problem where Julla has a specific amount of money in coins of different denominations. We'll break down the problem, provide a detailed solution, and ensure our answer is accurate.
Problem Overview
The problem at hand involves converting a total of 8.50 Peso into twenty-five centavo coins (25-cent pieces) and ten centavo coins (10-cent pieces), given that Julla has 8 more ten centavo coins than twenty-five centavo coins.
Given Information
Total amount in Pesos: 8.50 Number of 25-centavo coins: x Number of 10-centavo coins: y Julla has 8 more 10-centavo coins than 25-centavo coins (y x 8)Step-by-Step Solution
1. Define Variables: Let the number of 25-centavo coins be x and the number of 10-centavo coins be y.
2. Set Up Equations: Total amount in coins: 25x (25-centavo coins) 10y (10-centavo coins) 8.50 (850 centavos) Relationship between the number of coins: y x 8
3. Solve the System of Equations: Substitute y x 8 into the total amount equation: 25x 10( x 8) 850 Simplify the equation: 25x 1 80 850 Combine like terms: 35x 80 850 Subtract 80 from both sides: 35x 770 Solve for x: x 22
4. Find the Value of y: Substitute x 22 into the relationship equation: y x 8 y 22 8 30
5. Verify the Solution: Total amount: 25(22) 10(30) 550 300 850 centavos (8.50 Pesos) Number of coins: 22 x 25-centavo coins and 30 x 10-centavo coins
Conclusion
By following these steps, we can solve complex coin conversion problems using algebra. This method can be applied to similar problems involving different denominations and amounts. Understanding and solving problems like this can be extremely beneficial in everyday situations and financial planning.
Key Takeaways:
Using algebra to solve real-world problems involving money. Correctly defining variables and setting up equations based on given information. Checking solutions by substituting back into the original problem statement.For more practice, consider working through other coin conversion problems or exploring more advanced algebraic concepts.