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question:A British playwright is preparing for the opening night of their latest witty and satirical play. The theater has 20 rows of seats, with each row containing 15 seats. Tickets for each seat are priced at 8 pounds. On the opening night, 3/4 of the seats are sold. However, the playwright decides to give away 10 tickets to a group of local drama students as a gesture of goodwill. How much revenue does the playwright earn from ticket sales on the opening night?
answer:To solve this problem, let's follow these steps:1. Calculate the total number of seats in the theater: The theater has 20 rows, each with 15 seats. Therefore, the total number of seats is: [ 20 times 15 = 300 ]2. Determine the number of seats sold: On opening night, 3/4 of the seats are sold. So, the number of seats sold is: [ frac{3}{4} times 300 = 225 ]3. Account for the free tickets given away: The playwright gives away 10 tickets to drama students. Therefore, the number of seats actually sold for revenue is: [ 225 - 10 = 215 ]4. Calculate the revenue from the tickets sold: Each sold ticket is priced at 8 pounds. Thus, the total revenue is: [ 215 times 8 = 1720 ]The playwright earns a total revenue of 1720 pounds from ticket sales on the opening night.# 1720
question:The head chef at the Tomato and Egg Stir-Fry Chinese Restaurant is preparing for a busy weekend. On Saturday, the restaurant expects 120 customers, and on Sunday, they anticipate 150 customers. If each customer orders one serving of tomato and egg stir-fry, and each serving requires 2 eggs and 3 tomatoes, how many eggs and tomatoes will the chef need to order for the entire weekend?
answer:To solve this problem, we need to determine the total number of servings of tomato and egg stir-fry required for the weekend and then calculate the total number of eggs and tomatoes needed.Step 1: Calculate the total number of servings required for the weekend.- On Saturday, the restaurant expects 120 customers.- On Sunday, the restaurant anticipates 150 customers.Total servings for the weekend = servings on Saturday + servings on Sunday[ = 120 + 150 = 270]Step 2: Calculate the total number of eggs needed.- Each serving requires 2 eggs.- Total number of servings is 270.Total eggs needed = 270 servings × 2 eggs per serving[ = 540 text{ eggs}]Step 3: Calculate the total number of tomatoes needed.- Each serving requires 3 tomatoes.- Total number of servings is 270.Total tomatoes needed = 270 servings × 3 tomatoes per serving[ = 810 text{ tomatoes}]The chef needs to order 540 eggs and 810 tomatoes for the entire weekend.# 540 eggs and 810 tomatoes
question:Jamie is a film enthusiast who spends their weekends helping with film restoration and organizing screenings. On a particular Saturday, Jamie managed to restore 3 old films, each with a runtime of 90 minutes. After restoration, Jamie decided to organize a special screening event featuring these films. If Jamie plans to take a 15-minute break between each film during the screening event, how long will the entire event last, including the breaks?
answer:To solve the problem, we need to calculate the total time spent on the screening event, including the runtime of the films and the breaks between them.Step 1: Determine the total runtime of the films.- Each film has a runtime of 90 minutes.- Jamie restored 3 films.- The total runtime of the films is: ( 3 text{ films} times 90 text{ minutes/film} = 270 text{ minutes} ).Step 2: Determine the number of breaks and the total time for the breaks.- Jamie plans to take a 15-minute break between each film.- There are 3 films, which implies there will be breaks between the first and second film, and the second and third film.- The number of breaks is ( 3 - 1 = 2 ).- The total time for the breaks is: ( 2 text{ breaks} times 15 text{ minutes/break} = 30 text{ minutes} ).Step 3: Calculate the total duration of the event.- The total duration of the event is the sum of the total runtime of the films and the total time for the breaks.- Total event duration = Total film runtime + Total break time- Total event duration = ( 270 text{ minutes} + 30 text{ minutes} = 300 text{ minutes} ).Thus, the entire screening event, including the breaks, will last for a total of 300 minutes.# 300 minutes
question:Alex is a social media analyst who tracks the spread of misinformation online. One day, Alex notices that a false news story is shared 120 times in the first hour. During the second hour, the number of shares doubles, and in the third hour, the number of new shares is half of what it was in the second hour. However, Alex manages to successfully flag the story, reducing the number of new shares by 30 in the fourth hour. How many times is the news story shared in total by the end of the fourth hour?
answer:To solve the problem, let's break down the sharing pattern hour by hour.First Hour:- The news story is shared 120 times.Second Hour:- The number of shares doubles compared to the first hour.- Therefore, the number of shares in the second hour is (120 times 2 = 240).Third Hour:- The number of new shares is half of what it was in the second hour.- Therefore, the number of shares in the third hour is (frac{240}{2} = 120).Fourth Hour:- The number of new shares is reduced by 30 compared to the third hour.- Therefore, the number of shares in the fourth hour is (120 - 30 = 90).Now, let's calculate the total number of shares by adding up the shares from each hour:[text{Total Shares} = text{Shares in First Hour} + text{Shares in Second Hour} + text{Shares in Third Hour} + text{Shares in Fourth Hour}][text{Total Shares} = 120 + 240 + 120 + 90][text{Total Shares} = 570]Therefore, the news story is shared a total of 570 times by the end of the fourth hour.# 570
question:Mr. Thompson, a local shop owner in a small British town, is a strong supporter of Brexit and is keen on promoting British-made products in his store. He decides to rearrange his shop to highlight these products. Mr. Thompson has 120 shelves in his shop. He dedicates 3/4 of these shelves to British-made goods, and the rest to international products. If each shelf can hold 10 items, and he manages to fill 85% of the British shelves with items, how many British-made items does Mr. Thompson have on display in his shop?
answer:To solve this problem, we'll follow these steps:1. Calculate the number of shelves dedicated to British-made goods: Mr. Thompson dedicates 3/4 of his 120 shelves to British-made goods. We calculate the number of shelves as follows: [ text{Number of British shelves} = frac{3}{4} times 120 = 90 ]2. Determine the number of items that could be held on these British shelves: Each shelf can hold 10 items, so the maximum number of items these 90 shelves can hold is: [ text{Maximum number of British-made items} = 90 times 10 = 900 ]3. Calculate the actual number of British-made items on display: Mr. Thompson manages to fill 85% of the British shelves. Therefore, the number of British-made items actually on display is: [ text{Number of British-made items displayed} = 0.85 times 900 = 765 ]Therefore, the number of British-made items Mr. Thompson has on display in his shop is 765.# 765
question:Alex is an aspiring YouTuber who is passionate about creating content related to cooking. They are working on a video featuring five different recipes. For each recipe, Alex records two segments: a preparation segment that takes 15 minutes to film and a cooking segment that takes 30 minutes to film. After filming, Alex spends an additional 20 minutes editing each segment. If Alex films and edits all five recipes in one day, how many total minutes does Alex spend on filming and editing?
answer:To solve the problem, we need to calculate the total time Alex spends on both filming and editing all the segments for the five recipes.1. Understand the segments for each recipe: - Each recipe has two segments: a preparation segment and a cooking segment. - Preparation segment filming time: 15 minutes - Cooking segment filming time: 30 minutes2. Calculate the filming time for one recipe: - Total filming time per recipe = Preparation segment time + Cooking segment time - Total filming time per recipe = 15 minutes + 30 minutes = 45 minutes3. Calculate the total filming time for five recipes: - Total filming time for five recipes = 5 recipes × 45 minutes per recipe - Total filming time for five recipes = 225 minutes4. Understand the editing time for each segment: - Editing time per segment = 20 minutes5. Calculate the total number of segments for five recipes: - Each recipe has 2 segments (preparation and cooking) - Total number of segments for five recipes = 5 recipes × 2 segments per recipe - Total number of segments for five recipes = 10 segments6. Calculate the total editing time for all segments: - Total editing time = Total number of segments × Editing time per segment - Total editing time = 10 segments × 20 minutes per segment - Total editing time = 200 minutes7. Calculate the total time spent on filming and editing: - Total time = Total filming time + Total editing time - Total time = 225 minutes + 200 minutes - Total time = 425 minutesTherefore, the total time Alex spends on filming and editing all five recipes is 425 minutes.# 425