Problem 39 - Elementary Algebra

Question

Find the number of additional hours each year a student will spend in school if the average school day is increased to \(6.75\) hours. On average, U.S. students spend \(6.5\) hours per day in school, 180 days a year. That's far less than for students in many other developed nations. (Source: www.bnet.com, Jan. 28, 2008)

Step-by-Step Solution

Answer

45 additional hours per year.

Step 1 - Find the current total hours per year

Calculate the total hours the student currently spends in school per year. Multiply the current average hours per day (6.5) by the number of school days per year (180).\[6.5 \text{ hours/day} \times 180 \text{ days/year} = 1170 \text{ hours/year}\]

Step 2 - Find the proposed total hours per year

Now, calculate the total hours the student will spend in school per year if the school day is increased to 6.75 hours. Multiply the proposed average hours per day (6.75) by the number of school days per year (180).\[6.75 \text{ hours/day} \times 180 \text{ days/year} = 1215 \text{ hours/year}\]

Step 3 - Calculate the additional hours per year

Subtract the current total hours per year from the proposed total hours per year to find the additional hours the student will spend in school each year.\[1215 \text{ hours/year} - 1170 \text{ hours/year} = 45 \text{ additional hours/year}\]

Key Concepts

school hours calculation

Understanding the calculation of school hours is crucial to grasping this exercise. To determine the number of hours a student spends in school each year, we need to multiply the average number of hours per school day by the number of school days per year.
For instance, if the average school day is 6.5 hours and a student attends school 180 days a year, the total hours per year would be computed as follows: \[6.5 \text{ hours/day} \times 180 \text{ days/year} = 1170 \text{ hours/year}\] This means the student spends 1,170 hours in school annually under the current schedule. Understanding this multiplication process helps in establishing a base to compare with any proposed changes to the school hours.
Once we know the current total hours, we can repeat the process for any proposed changes, such as increasing the school day to 6.75 hours. Applying similar multiplication gives us the new total hours spent each year.

multiplication in algebra

Multiplication is a fundamental algebraic operation that helps in calculating totals. In the context of this problem, we use multiplication to find the total number of school hours per year. When given the average hours per day and the number of school days, we multiply these two values to get the annual total.
For example, consider the calculation: \[6.5 \text{ hours/day} \times 180 \text{ days/year} = 1170 \text{ hours/year}\] Here, we multiply 6.5 by 180 to get 1,170, which represents the total school hours for the year. This operation is straightforward but essential, especially when comparing different scenarios, such as proposed changes to school schedules. Multiplication in algebra is not only about combining numbers but also about understanding how these numbers represent real-world quantities, such as total time spent in school.
By mastering this concept, students can effectively apply it to various problems, making complex calculations much simpler and more intuitive.

subtraction in algebra

Subtraction is another key algebraic concept used to find differences between quantities. In the context of our exercise, we use subtraction to determine the additional hours students will spend in school when there's a change in the daily schedule.
After calculating the current and proposed total school hours per year, we subtract the current total from the proposed total to find the difference: \[1215 \text{ hours/year} - 1170 \text{ hours/year} = 45 \text{ additional hours/year}\] This tells us that students will spend 45 more hours in school each year if the school day increases from 6.5 to 6.75 hours.
Understanding this subtraction process helps students see how differences in schedules impact total yearly hours. It also emphasizes the importance of precise calculations in comparing different scenarios and making informed decisions. Subtraction, just like addition and multiplication, is a basic but crucial part of problem-solving in algebra and everyday life scenarios.