Quarters and Dimes: A Comprehensive Guide to Achieving exactly $5.65

In this article, we will explore how to determine the number of quarters needed to reach a specific dollar amount, using a real-world example. We'll also break down the reasoning and calculations involved to ensure a thorough understanding.

Understanding the Problem

The problem at hand involves converting 24 dimes into quarters to achieve a total of $5.65. This is a common type of problem in basic arithmetic and can help enhance understanding of money and value conversion. Let's dive into the calculations step by step.

Calculation Breakdown

1. **Convert Dimes to Dollars:**

First, we convert the 24 dimes into dollars. Since 1 dime is worth $0.10, the calculation is straightforward:

24 dimes times; $0.10/dime $2.40

This means that 24 dimes are worth $2.40.

2. **Determine the Remaining Amount Needed:**

Next, we need to find out how much more we need to reach $5.65. Subtract the value of the dimes from the target amount:

$5.65 - $2.40 $3.25

So, we need an additional $3.25 to reach the target amount of $5.65.

3. **Converting the Remaining Amount to Quarters:**

Quarters are worth $0.25 each. To find out how many quarters are needed to make up $3.25, we divide the remaining amount by the value of one quarter:

$3.25 divide; $0.25/quarter 13 quarters

This means that we need 13 quarters to make up the remaining amount of $3.25.

Conceptual Understanding

Let's break down the problem conceptually with the given premises and assumptions:

PREMISES

24 dimes 240.10 times; 0.10 $2.40 $5.65 - $2.40 $3.25 $3.25 divide; $0.25 13 quarters

1. Let D the number of dimes, which is 24.

2. Let Q the number of quarters, which we need to determine.

3. We need to find the value of Q in dollars, knowing that each quarter is worth $0.25.

ASSUMPTIONS

Each dime is worth $0.10. Each quarter is worth $0.25.

4. We assume that we are dealing with standard US currency values and that the conversion is straightforward.

CALCULATIONS

24 dimes 24 times; $0.10 $2.40 $5.65 - $2.40 $3.25 $3.25 divide; $0.25 13 quarters

By subtracting the value of the dimes from the target amount, we determine the remaining amount in dollars. Dividing this by the value of each quarter gives us the number of quarters needed.

PROOF

$2.40 13 quarters times; $0.25 $5.65 $2.40 $3.25 $5.65

This confirms that 13 quarters are indeed needed to reach the total of $5.65.

Conclusion

Therefore, to achieve a total of $5.65 using 24 dimes, you need 13 quarters. Understanding these calculations can be beneficial for both practical and educational purposes, helping you manage and understand monetary values better.

Keywords: quarters, dimes, number of quarters