Solving the Cost of a Shirt and Tie Problem: A Step-by-Step Guide

Let's explore a classic problem that involves finding the cost of a shirt when given the total cost and a relationship between the costs of two items. This article will walk through the problem-solving process systematically, using algebraic equations for clarity and precision.

Problem Statement

Consider the following problem statement:

A shirt and a tie together cost 50 dollars. The shirt costs 30 dollars more than the tie. What is the cost of the shirt?

Understanding the Problem

We have two main pieces of information from which we can derive equations:

The total cost of the shirt and tie is $50.00. The shirt costs $30.00 more than the tie.

Let's define the variables and set up our equations:

Preliminaries

Let:

S represent the cost of the shirt in dollars. T represent the cost of the tie in dollars.

Setting Up Equations

Based on the problem statement, we can establish the following equations:

Total cost of the shirt and tie:

S T $50.00

The shirt costs $30.00 more than the tie:

S T $30.00

Solving the Equations

We can substitute the second equation into the first to solve for T and then find S.

Step-by-Step Solution

Substitute S T 30 into the total cost equation:

T 30 T 50

Simplify the equation by combining like terms:

2T 30 50

Solve for T by isolating the variable:

2T 50 - 30 20

T 20 / 2 10

Now that we know the cost of the tie, we can find the cost of the shirt:

S T 30 10 30 40

Verification

To ensure the solution is correct, let's verify by checking the total cost:

Cost of the shirt: $40.00 Cost of the tie: $10.00 Total: 40 10 50

The solution is correct, and the cost of the shirt is $40.00.

Conclusion

In this article, we demonstrated how to solve a classic algebraic problem by setting up and solving a system of equations. The cost of the shirt is $40.00, which satisfies both conditions given in the problem statement.

Additional Context

For those who enjoy wearing business attire daily, understanding the cost breakdown can be crucial. Consider the following additional context:

A business suit can cost upwards of $300. Shirts can range between $80 and $150. Dress shoes can cost around $125. Ties usually range between $50 and $200. Coats can be $300 or more.

These higher-end options often make a significant difference in one's professional appearance and can justify the additional expense for those who prioritize quality and style.