Problem 440 - Prealgebra

Question

Dental floss One package of dental floss is 54 feet long. Brian uses 2 feet of dental floss every day. How many days will one package of dental floss last Brian?

Step-by-Step Solution

Answer

27 days

Step 1 - Understand the problem

Determine the total length of the dental floss and how much floss Brian uses per day. The total length of the floss is 54 feet and Brian uses 2 feet per day.

Step 2 - Set up the equation

To find out how many days the floss will last, we need to divide the total length of the floss by the amount used per day. This can be expressed as: \[ \text{Number of days} = \frac{\text{Total length of floss}}{\text{Floss used per day}} \]Substitute the given values: \[ \text{Number of days} = \frac{54 \text{ feet}}{2 \text{ feet/day}} \]

Step 3 - Perform the division

Carry out the division to solve for the number of days:\[ \text{Number of days} = \frac{54}{2} = 27 \]

Step 4 - Interpret the result

The result of the division tells us how many days the dental floss will last Brian. Therefore, one package of dental floss will last Brian for 27 days.

Key Concepts

basic arithmetic

Understanding basic arithmetic is essential for solving many everyday problems. Here, Brian's use of dental floss is an excellent example.
To solve how long the dental floss will last Brian, we need to use basic division. The problem provides these key pieces of information:

• The total length of the dental floss: 54 feet
• The amount of dental floss used per day: 2 feet

We can find the number of days the dental floss will last by dividing the total length by the length used each day. In mathematical terms, this is written as:
\[\text{Number of days} = \frac{\text{Total length of floss}}{\text{Floss used per day}}\]Substituting the given values, we have:
\[\text{Number of days} = \frac{54 \text{ feet}}{2 \text{ feet/day}} = 27 \text{ days}\]Thus, the basic arithmetic operation of division helps us easily determine that one package of dental floss will last Brian 27 days.

problem-solving

Problem-solving is the process of identifying solutions to specific issues. Here, to determine how many days Brian's dental floss will last, we approached the problem using a systematic method.
First, we gathered all relevant details: the total length of dental floss (54 feet) and the daily consumption (2 feet per day). Then, we set up an equation to represent the scenario mathematically. This helps clarify how the values relate to each other.
The equation we crafted was simple:
\[\text{Number of days} = \frac{\text{Total length of floss}}{\text{Floss used per day}}\]By substituting the provided values, we resolved the equation to find the solution. This step-by-step approach illustrates the importance of breaking down problems into manageable parts, solving a small piece at a time and ensuring each part is correct. This methodical approach is invaluable for tackling more complex problems.

unit rates

Unit rates are foundational in understanding how quantities relate to one another. In this example, the unit rate is the amount of dental floss used per day, which is 2 feet per day.
This unit rate tells us how much floss Brian uses each day, making it easier to calculate how long the total supply will last. The term 'unit rate' helps us understand that, for each day, a specific amount of dental floss (2 feet) is consumed.
When we combine unit rates with the total quantity, we can find out how long the total quantity will last. The calculation involves dividing the total amount (54 feet) by the rate of consumption (2 feet/day):
\[\text{Number of days} = \frac{54 \text{ feet}}{2 \text{ feet/day}} = 27 \text{ days}\]Therefore, understanding unit rates allows us to approach and solve such problems easily and accurately. This foundational concept is not only useful in math but also helps make informed decisions in daily life.