Problem 30 - Prealgebra

Question

If a 15 -day supply of vitamins costs \(\$ 1.62\) what is the price in cents per day?

Step-by-Step Solution

Answer

The price is 10.8 cents per day.

Step 1: Convert Dollars to Cents

First, we need to convert the total cost from dollars to cents. We know that 1 dollar is equal to 100 cents, so multiply 1.62 dollars by 100 to convert it to cents.

Step 2: Calculate Total Cost in Cents

Perform the calculation: \[ 1.62 \times 100 = 162 \text{ cents} \]The total cost is 162 cents.

Step 3: Determine Cost Per Day

Divide the total amount in cents by the number of days (15) to find out the cost per day in cents:\[ \frac{162}{15} = 10.8 \text{ cents} \]The cost per day is 10.8 cents.

Key Concepts

Decimal Conversion

In the world of mathematics and everyday finance, decimal conversion plays a crucial role. When dealing with currency, it's often necessary to convert dollars into smaller units, such as cents, to simplify calculations. This is especially useful when making exact calculations or comparisons involving unit costs.

For instance, 1 dollar is equivalent to 100 cents. Therefore, when converting a value of 1.62 dollars into cents, you need to multiply by 100. This is because there are 100 cents in each dollar. So, the conversion for 1.62 dollars to cents would be computed as follows:

• Multiply 1.62 by 100
• This results in 162 cents

By understanding the basics of decimal conversion, you ensure accuracy in financial calculations. This process is essential in facilitating more straightforward and precise budgeting and expense tracking.

Division Operation

Division is a fundamental arithmetic operation used in many real-life applications, including determining unit rates. When you need to find a unit rate, such as price per day or speed, division is how you obtain that rate.

In our example of the cost analysis of vitamins, once you have the total cost in cents, which is 162 cents, you use division to determine how much you would spend per day over a given period. The operation looks like this:

• Take the total amount in cents: 162
• Divide by the number of days: 15

The calculation becomes \[\frac{162}{15} = 10.8 \,\text{cents per day}\]The result, 10.8 cents per day, tells you how much one day's worth of vitamins costs. This operation simplifies understanding of costs over longer periods by breaking down the total into easily digestible amounts. Mastering division not only facilitates better understanding but also improves your problem-solving skills, enabling you to handle a variety of practical scenarios.

Cost Analysis

Conducting a cost analysis is crucial for making informed purchasing decisions. It involves breaking down the total cost into smaller parts to understand the price of each component or unit fully. In the given problem, you analyze the cost per day of a 15-day vitamin supply.

To do this, first convert the total expense from dollars to cents for simplification and accuracy. Then, you divide this total amount by the number of days to find the daily cost. This method allows you to see how much each day's vitamins cost, providing a clearer picture of the overall daily expense.

• This analysis helps in budgeting.
• It enables you to compare prices easily when purchasing in different sizes or quantities.
• Helps in understanding whether buying in bulk offers any significant savings or not.

By performing such cost analyses regularly, you make more informed financial decisions, ensuring efficient management of finances and resources.