Expressing the Total Peso Value of 20 Coins in Mathematical Form

When dealing with monetary values and coin combinations, it's often necessary to express the total value in a mathematical form. This article will guide you through the process of expressing the total peso value of 20 coins, consisting of both PHP 5 and PHP 10 coins, in a mathematical expression.

Introduction

The problem at hand involves determining the total value of a set of 20 coins, where the coins consist of two denominations: PHP 5 and PHP 10. The challenge lies in expressing the total value using a mathematical equation that accurately represents the total peso value of the coins. This is particularly useful in various fields, including finance, mathematics, and economics.

Mathematical Approach

To solve this problem, we can use a system of linear equations. Let's define the variables and derive the equation step-by-step.

Defining the Variables

Let:

x the number of 10 peso coins y the number of 5 peso coins

Given that the total number of coins is 20, we have the first equation:

x y 20

Next, we need to express the total value of the coins. The total value in pesos can be represented as:

Total Value 1 5y

solving the system of equations

To find a more concise form of the expression, we can use the first equation to express one variable in terms of the other. Let's express y in terms of x:

y 20 - x

Substituting this into the total value equation:

Total Value 1 5(20 - x)

Expanding the expression:

Total Value 1 100 - 5x

Combining like terms:

Total Value 5x 100

Thus, the mathematical expression that represents the total peso value of the 20 coins is:

V 5x 100

Alternative Formulations

The alternative formulation provided, 5x 10y 20, represents another approach to solving the problem. However, it does not directly give the total value. Instead, it can be used to find the possible combinations of x and y. Let's explore this further:

Using the alternative formulation

The equation 5x 10y 20 can be simplified by dividing every term by 5:

x 2y 4

This equation represents the relationship between the number of 5 peso coins and the number of 10 peso coins. Some possible solutions to this equation are:

x 4, y 0 (4 coin 10 peso, 0 coin 5 peso) x 2, y 1 (2 coin 10 peso, 1 coin 5 peso) x 0, y 2 (0 coin 10 peso, 2 coin 5 peso)

Each solution gives a different combination that satisfies the total number of coins being 20. However, the expression V 5x 100 directly gives the total value for each combination.

Conclusion

Expressing the total peso value of 20 coins consisting of PHP 5 and PHP 10 coins in a mathematical form is a valuable exercise for understanding the relationship between the quantities and the total value. The final expression V 5x 100 provides a straightforward way to calculate the total value, while the alternative formulation 5x 10y 20 can be used to find possible combinations of the coins.

By mastering these mathematical expressions, you can accurately determine the total value of any combination of coins and extend this knowledge to various real-world applications.