Solving Carrie's Book Buying Dilemma: A Mathematical Exploration

Have you ever found yourself in a situation where you're trying to figure out the cost of an item based on certain conditions? This is exactly what Carrie faced. In this article, we will explore the mathematical problem she encountered and the steps to solve it. Let's break down the situation and dive deep into the logic behind it.

The Problem

Carrie wanted to buy 9 books but was 12 dollars short. Instead, she decided to buy 4 books and had $38 left over. The question is, what was the cost of each book?

Step-by-Step Solution

Let's denote the total amount of money Carrie has as y and the cost of each book as x. The problem can be formulated as two simultaneous equations:

1. 9x - y 12

2. y - 4x 38

Understanding the Equations

From the first equation, we can see that the cost of 9 books is $12 more than the total amount of money Carrie has. This can be expressed as:

9x y 12

From the second equation, we can see that buying 4 books leaves her with $38:

y - 4x 38

Solving the Equations

Now, let's solve these equations step-by-step:

Rearrange the first equation to express y in terms of x:

y 9x - 12

Substitute y from the above equation into the second equation:

(9x - 12) - 4x 38

Simplify the equation:

5x - 12 38

5x 50

x 10

Now that we have the value of x, we can substitute it back into the first equation to find y:

y 9x - 12

y 9(10) - 12

y 90 - 12

y 78

Therefore, the cost of each book is $10, and Carrie has a total of $78.

Verifying the Solution

To ensure our solution is correct, let's verify it:

The cost of 9 books is 9 * 10 $90. Since Carrie is short by $12, her total amount of money is:

$90 - $12 $78

Buying 4 books at $10 each costs:

4 * 10 $40

After purchasing 4 books, she has:

$78 - $40 $38 left over

Both conditions of the problem are satisfied, confirming our solution is correct.

Conclusion

Through this problem, we have explored the practical application of simultaneous equations and how they can be used to solve real-life scenarios. By understanding the relationships between the variables and solving the equations step-by-step, we can find the solution efficiently.

Keywords

math problem, simultaneous equation, price calculation