Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise.
A shirt and a tie together cost $53. The shirt costs $21 more than the tie. What is the cost of the shirt?
$ 
37
 
Correct: Your answer is correct.

Polya’s four-step problem-solving strategy can be applied to this problem as follows:

### Step 1: Understand the problem
We are given:
- The combined cost of a shirt and a tie is $53.
- The shirt costs $21 more than the tie.
We are tasked with finding the cost of the shirt.

### Step 2: Devise a plan
Let’s define:
- $ x $ as the cost of the tie.
- The shirt costs $21 more than the tie, so the cost of the shirt is $ x + 21 $.
The total cost of both the shirt and the tie is $53, so we can form the equation:
\[
x + (x + 21) = 53
\]
This equation will help us find $ x $, the cost of the tie, and then we can use it to find the cost of the shirt.

### Step 3: Carry out the plan
Simplify and solve the equation:
\[
2x + 21 = 53
\]
Subtract 21 from both sides:
\[
2x = 32
\]
Divide by 2:
\[
x = 16
\]
So, the cost of the tie is $16.

Now, the cost of the shirt is $ 16 + 21 = 37 $.

### Step 4: Look back
Check the solution:
- The tie costs $16.
- The shirt costs $37, which is $21 more than the tie.
- The total cost is $ 16 + 37 = 53 $, which matches the problem statement.

Thus, the cost of the shirt is indeed $37.

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Would you like more details on this solution or clarification on any part of it?

Here are some related questions to explore:

1. What if the shirt was $25 more than the tie? How would that change the equation?
2. If the shirt and tie together cost $70, with the same $21 difference, what would the cost of the shirt be?
3. How can we apply Polya’s four-step strategy to more complex problems?
4. What if the tie cost $30, and the shirt was a percentage more expensive?
5. How would this problem change if both items had a 10% sales tax?

**Tip:** Always verify your solution by plugging it back into the original problem to ensure accuracy.

A shirt and a tie together cost $53. The shirt costs $21 more than the tie. What is the cost of the shirt?

Learn how to solve a linear equation where a shirt and tie cost $53 together, with the shirt costing $21 more than the tie. This problem explores key algebraic concepts and is suitable for students in Grades 6-8.

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