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question:Mr. Algebra, the patient algebra teacher, wants to illustrate the concept of multiplication using everyday classroom scenarios to make the subject interesting for his students. He decides to use the number of students in his class and the number of pens each student needs for their projects. If Mr. Algebra has 24 students in his class, and he wants to give each student 3 pens, how many pens does Mr. Algebra need in total to ensure every student has enough pens for their projects?
answer:To find out how many pens Mr. Algebra needs in total, we need to multiply the number of students by the number of pens each student requires.Step 1: Identify the number of students.- Mr. Algebra has 24 students in his class.Step 2: Identify the number of pens each student needs.- Each student needs 3 pens.Step 3: Multiply the number of students by the number of pens each student needs.- Calculation: ( 24 text{ students} times 3 text{ pens per student} = 72 text{ pens} ).Therefore, Mr. Algebra needs a total of 72 pens to ensure every student has enough for their projects.# 72
question:The local economic development board is working on a plan to attract financial institutions to a rural community. They estimate that each new financial institution will create 15 new jobs. The board aims to bring in 4 new banks and 3 credit unions to the area. Additionally, each bank is expected to generate 200,000 in local revenue annually, while each credit union is expected to generate 150,000. How many new jobs will be created, and what will be the total expected annual local revenue from these financial institutions?
answer:To solve this problem, we need to calculate two separate quantities: the number of new jobs created and the total expected annual local revenue from the new financial institutions.Step 1: Calculate the number of new jobs created.Each financial institution creates 15 new jobs. The board aims to bring in 4 new banks and 3 credit unions. - Total number of financial institutions = 4 banks + 3 credit unions = 7 financial institutions.- Total number of new jobs = 7 financial institutions × 15 jobs per institution = 105 jobs.Step 2: Calculate the total expected annual local revenue.Each bank generates 200,000 in local revenue annually, and each credit union generates 150,000.- Total revenue from banks = 4 banks × 200,000 per bank = 800,000.- Total revenue from credit unions = 3 credit unions × 150,000 per credit union = 450,000.- Total expected annual local revenue = 800,000 + 450,000 = 1,250,000.Thus, we have:- New jobs created: 105 jobs- Total expected annual local revenue: 1,250,000# 105 jobs, 1,250,000 total annual revenue
question:A seasoned contributor at Arcan and Durden spends 15 hours a week mentoring a new user. In addition to mentoring, they dedicate 10 hours a week to writing articles and 5 hours a week to reviewing content. If they decide to spend an extra 2 hours each week mentoring, how many hours will they be spending on all their activities in total each week?
answer:To solve the problem, we need to calculate the total number of hours the contributor spends on all activities per week, given the changes in their mentoring time.1. Current Hours of Mentoring: The contributor currently spends 15 hours a week mentoring a new user.2. Additional Mentoring Hours: They decide to spend an extra 2 hours each week on mentoring. So, the new mentoring time will be: ( 15 text{ hours} + 2 text{ hours} = 17 text{ hours} )3. Hours Spent on Other Activities: - Writing articles: 10 hours per week - Reviewing content: 5 hours per week4. Calculate Total Hours: To find the total number of hours spent on all activities, we add up the hours for each activity: [ text{Total hours} = text{Mentoring hours} + text{Writing hours} + text{Reviewing hours} ] [ text{Total hours} = 17 text{ hours} + 10 text{ hours} + 5 text{ hours} ]5. Perform the Addition: [ text{Total hours} = 17 + 10 + 5 = 32 text{ hours} ]The contributor will spend a total of 32 hours on all activities each week.# 32
question:A traditional freight brokerage owner, Mr. Thompson, is curious to compare his current business model to a new digital freight platform. He manages 50 shipments per week manually and earns a profit of 100 per shipment. He learns that the digital model promises to increase his shipments by 30% while reducing his profit per shipment by 10 due to platform fees.Mr. Thompson wants to know how much more profit he could potentially earn in a week using the digital model compared to his current method. How much profit does Mr. Thompson earn with each model, and what is the difference in profit between the two models?
answer:To solve this problem, we need to calculate the weekly profit for both the traditional and digital freight brokerage models and then find the difference in profit between the two models.Step 1: Calculate the profit for the traditional model.- Number of shipments per week (traditional model) = 50- Profit per shipment (traditional model) = 100The total weekly profit for the traditional model is calculated as follows:[text{Total Profit (Traditional)} = text{Number of Shipments} times text{Profit per Shipment}][text{Total Profit (Traditional)} = 50 times 100 = 5000]Step 2: Calculate the profit for the digital model.- Increase in shipments = 30% of 50 shipments- New number of shipments per week (digital model) = 50 + 0.30 times 50Calculating the increase in shipments:[text{Increase in Shipments} = 0.30 times 50 = 15]Calculating the new number of shipments per week:[text{New Number of Shipments} = 50 + 15 = 65]- New profit per shipment (digital model) = 100 - 10 = 90The total weekly profit for the digital model is calculated as follows:[text{Total Profit (Digital)} = text{New Number of Shipments} times text{New Profit per Shipment}][text{Total Profit (Digital)} = 65 times 90 = 5850]Step 3: Calculate the difference in profit between the two models.[text{Difference in Profit} = text{Total Profit (Digital)} - text{Total Profit (Traditional)}][text{Difference in Profit} = 5850 - 5000 = 850]Thus, Mr. Thompson could potentially earn 850 more in profit per week using the digital model compared to his current method.# 850
question:Sarah owns a bookstore in a historic building that is 120 years old. She is planning to restore the building to preserve its original charm. The restoration project is estimated to cost 45,000. To raise funds, Sarah decides to hold a special sale where she offers a 20% discount on all books. If the average price of a book before the discount is 25 and she expects to sell 400 books during the sale, how much money will she need to raise from other sources to cover the full restoration cost?
answer:To solve this problem, we need to determine how much money Sarah will raise from the sale and then calculate how much additional money she will need to cover the full restoration cost.Step 1: Calculate the discount amount.The discount Sarah is offering is 20%. Therefore, the discount amount on the average price of a book is:[text{Discount amount} = 0.20 times 25 = 5]Step 2: Calculate the sale price per book.The sale price per book after the discount is:[text{Sale price per book} = 25 - 5 = 20]Step 3: Calculate the total revenue from selling 400 books.Sarah expects to sell 400 books at the sale price of 20 each. Thus, the total revenue from the sale is:[text{Total revenue} = 400 times 20 = 8000]Step 4: Determine the additional funds needed.The total restoration cost is 45,000. Sarah's sale will generate 8,000. Therefore, the amount she still needs to raise from other sources is:[text{Additional funds needed} = 45000 - 8000 = 37000]# 37000
question:A successful author of dystopian novels is crafting a new book and wants to create a captivating world with a unique society structure. In the society, there are 3 distinct classes: Innovators, Preservers, and Reformers. There are twice as many Innovators as there are Preservers, and the number of Reformers is 10 more than the number of Innovators. If the total population of this society is 210 individuals, how many individuals are there in each class?
answer:To solve this problem, we need to define variables for each class and set up equations based on the given relationships. Let's define the variables as follows:- Let ( P ) represent the number of Preservers.- Since there are twice as many Innovators as there are Preservers, let ( I = 2P ) represent the number of Innovators.- The number of Reformers is 10 more than the number of Innovators, so let ( R = I + 10 ).According to the problem, the total population of the society is 210 individuals. Therefore, we have the equation:[I + P + R = 210]Substituting the expressions for ( I ) and ( R ) in terms of ( P ) into the equation, we get:[2P + P + (2P + 10) = 210]Simplifying the equation:[5P + 10 = 210]Subtract 10 from both sides to isolate the term with ( P ):[5P = 200]Divide both sides by 5 to solve for ( P ):[P = 40]Now that we have ( P ), we can determine ( I ) and ( R ):- Innovators (( I )): ( I = 2P = 2 times 40 = 80 )- Reformers (( R )): ( R = I + 10 = 80 + 10 = 90 )Thus, the number of individuals in each class is:- Innovators: 80- Preservers: 40- Reformers: 90To verify, we check that the total population sums to 210:[I + P + R = 80 + 40 + 90 = 210]The solution checks out. Therefore, the final answer is:# 80, 40, 90