answer:Let's break down Mary's book acquisitions and losses throughout the year: 1. She started with 72 mystery books. 2. She received 1 book per month for 12 months from her book club, totaling 12 books. 3. She purchased 5 books from a bookstore. 4. Her daughter gave her 1 book for her birthday. 5. Her mother gave her 4 books during a visit. 6. In total, she received 72 + 12 + 5 + 1 + 4 = 94 books. Additionally, Mary donated 12 books and sold 3 books, resulting in a net loss of 12 + 3 = 15 books. To find out how many books Mary has at the end of the year, subtract the net loss (15) from her total book acquisitions (94): 94 - 15 = 79 books Mary has 79 books in her library at the end of the year.,Mary starts with 72 books. She receives 1 book per month for 12 months, so she receives 1 x 12 = 12 books from her book club. She purchases 5 books from a bookstore and 2 books from yard sales, so she adds 5 + 2 = 7 books to her collection. Her daughter gives her 1 book for her birthday and her mother gives her 4 books during a visit, so she adds 1 + 4 = 5 books to her collection. She donates 12 books to a charity shop and sells 3 books to a used book store, so she subtracts 12 + 3 = 15 books from her collection. To find the total number of books at the end of the year, we add the initial number of books to the books she received and purchased and subtract the books she donated and sold: 72 + 12 + 7 + 5 - 12 - 3 = 81. Mary has 81 books in her library at the end of the year. 81 The answer is: 81, Here's the calculation to determine how many books Mary has at the end of the year: 1. At the beginning of the year, Mary had 72 mystery books. 2. She received 1 book per month from her book club for 12 months, so that's an additional 12 books. 3. Halfway through the year, she purchased 5 books from a bookstore. 4. Later on, she purchased 2 books from yard sales. 5. Her daughter gave her 1 book for her birthday, and her mother gave her a series of 4 books during a visit. 6. This brings the total number of books she gained during the year to: 72 (initial) + 12 (book club) + 5 (bookstore) + 2 (yard sales) + 1 (daughter) + 4 (mother) = 96 books. 7. However, she also donated 12 books to a charity shop and sold 3 books to a used book store. 8. So, we need to subtract those books from the total: 96 - 12 (donated) - 3 (sold) = 81 books. Therefore, Mary has 81 books in her library at the end of the year.

answer:If Tracy collected a certain number of books in the first week, and ten times as many books in the next five weeks, then the total number of books she collected in the first week and the next five weeks is 1 + 10 = 11 times the number of books she collected in the first week. If Tracy currently has 99 books, then the total number of books she collected in the first week and the next five weeks is 99 books. So, the number of books she collected in the first week is 99 books / 11 = 9 books. 9 The answer is: 9, To find out how many books Tracy collected during the first week, we need to determine the number of books she collected in the next five weeks and then find out what number, when increased by a factor of 10, would result in the total number of books she currently has. Let's denote the number of books Tracy collected during the first week as x. The number of books she collected in the next five weeks would be 10 * x (ten times the number collected in the first week). Now, let's calculate the total number of books Tracy has: Total books = Books from week 1 + Books from weeks 2-6 = x + 10x = 11x According to the problem, Tracy currently has 99 books, so: 11x = 99 Now, let's solve for x: x = 99 / 11 x = 9 So, Tracy collected 9 books during the first week.,Let x be the number of books Tracy collected in the first week. In the next five weeks, she collected 10x books. So, the total number of books she has after six weeks is: x (from the first week) + 10x (from the next five weeks) = 99 Combining the terms, we get: 11x = 99 Now, we can solve for x by dividing both sides by 11: x = 99 / 11 x = 9 So, Tracy collected 9 books in the first week.

answer:If Dean takes 9 hours to complete the marathon, Micah runs 2/3 times as fast as Dean, so Micah takes 9 * 2/3 = 6 hours to complete the marathon. Jake takes 1/3 times more time than Micah, so Jake takes 6 + 1/3 * 6 = 6 + 2 = 8 hours to complete the marathon. To find the total time the three take to complete the marathon, we add the individual times: 9 + 6 + 8 = 23 hours. Therefore, the total time the three take to complete the marathon is 23 hours. 23 The answer is: 23, First, we need to determine the time it takes Micah to run the marathon. Since Micah runs 2/3 times as fast as Dean, this means that Micah takes 3/2 the time Dean takes: Micah's time = (3/2) * Dean's time = (3/2) * 9 hours = 13.5 hours Next, we need to determine the time it takes Jake to run the marathon. Jake takes 1/3 times more time than Micah to finish the marathon: Jake's time = (1 + 1/3) * Micah's time = (4/3) * 13.5 hours = 18 hours Now, we add up the time it takes for each of them to run the marathon: Total time = Micah's time + Dean's time + Jake's time = 13.5 hours + 9 hours + 18 hours = 34.5 hours Therefore, it takes the three of them a total of 34.5 hours to complete the marathon.,Let's use variables to represent the times it takes each person to complete the marathon. Let D be the time it takes Dean to complete the marathon (9 hours). Let M be the time it takes Micah to complete the marathon. Let J be the time it takes Jake to complete the marathon. We are given that Micah runs 2/3 times as fast as Dean, so: M = 2D/3 And it takes Jake 1/3 times more time to finish the marathon than it takes Micah, so: J = M + (1/3)M Since we know Dean's time (D = 9), we can find Micah's time: M = 2D/3 = 2(9)/3 = 6 Now, we can find Jake's time by substituting Micah's time back into the equation: J = M + (1/3)M = 6 + (1/3)6 = 6 + 2 = 8 Now we know all three times: D = 9 hours M = 6 hours J = 8 hours To find the total time, we simply add these times together: Total time = D + M + J = 9 + 6 + 8 = 23 hours So, the total time Micah, Dean, and Jake take to complete the marathon is 23 hours.

answer:To solve this problem, we need to determine the value of x, which represents the estimated time left for the bus journey in minutes. Let's break down the given information: - Harry has already been on the bus for 15 minutes. - The remaining bus journey will take x minutes. - The walk from the bus stop to his house will take half the time of the bus journey. - In total, Harry will spend 60 minutes traveling. Now, let's set up an equation using the given information: 15 minutes (already spent on the bus) + x minutes (remaining bus journey) + (1/2) * (bus journey time) (walking time) = 60 minutes (total traveling time) We can rearrange this equation to solve for x: 15 + x + (1/2) * (x) = 60 To solve for x, let's first multiply (1/2) * (x) and combine the terms: 15 + (1 + 1/2) * x = 60 15 + (3/2) * x = 60 Now, to isolate x, we need to subtract 15 from both sides of the equation: 15 + (3/2) * x - 15 = 60 - 15 (3/2) * x = 45 Next, we need to divide both sides of the equation by (3/2): (3/2) * x / (3/2) = 45 / (3/2) x = 45 / (3/2) Simplify the fraction: x = 45 * (2/3) x = 30 Therefore, the value of x is 30 minutes. The remaining bus journey will take 30 minutes, and the total bus journey will be 15 + 30 = 45 minutes., The total time Harry spends traveling is 60 minutes, which consists of the x minutes bus ride and half of that time as a walk to his house. Therefore, we can write the equation: x + x/2 = 60 Multiplying both sides by 2 to get rid of the fraction, we have: 2x + x = 120 3x = 120 x = 40 So, the bus journey takes 40 minutes, and the walk from the bus stop to his house takes 20 minutes.,To solve this problem, we need to determine the value of x, which represents the remaining time of the bus journey. Let's break down the information given: Time already spent on the bus: 15 minutes Remaining time of the bus journey: x minutes Time spent walking from the bus stop to the house: 1/2 * time spent on the bus Total time spent traveling: 60 minutes We can set up the equation as follows: Time already spent on the bus + Remaining time of the bus journey + Time spent walking = Total time spent traveling 15 + x + 1/2 * (15 + x) = 60 Let's simplify and solve for x: 15 + x + 7.5 + 1/2x = 60 To combine like terms, let's multiply 1/2 by (15 + x): 15 + x + 7.5 + 0.5x = 60 To simplify, let's combine like terms: 1.5x + 22.5 = 60 To isolate x, we subtract 22.5 from both sides of the equation: 1.5x + 22.5 - 22.5 = 60 - 22.5 1.5x = 37.5 To solve for x, we divide both sides of the equation by 1.5: x = 37.5 / 1.5 x = 25 The value of x is 25. 25 The answer is: 25