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question：Alex has a bag of apples. She gives her brother 48 apples, gives her sister three times as many apples as she gave her brother, and gives one-quarter of the amount of apples she gave her sister to her friend. How many apples does Alex have left if the bag originally contains 420 apples?
answer：First, I need to determine how many apples Alex gave to her sister. Since she gave her brother 48 apples and her sister received three times that amount, I multiply 48 by 3 to find out the number of apples given to her sister.Next, I calculate the number of apples Alex gave to her friend. The friend received one-quarter of the apples that were given to the sister, so I take one-quarter of the amount calculated in the previous step.After finding out how many apples were given to the brother, sister, and friend, I add all these amounts together to find the total number of apples given away.Finally, I subtract the total number of apples given away from the original number of apples in the bag to determine how many apples Alex has left.
question：Alex is a government intelligence analyst who has received 120 pages of translated data to review. To efficiently prioritize the analysis, Alex decides to split the data into sections of high, medium, and low priority. Alex assigns 40% of the pages to high priority, 30% to medium priority, and the remaining pages to low priority. How many pages are assigned to each priority category?
answer：First, I need to determine the number of pages assigned to each priority category based on the given percentages.Alex has a total of 120 pages to review.For high priority, 40% of the pages are assigned. To find this, I'll calculate 40% of 120.Next, for medium priority, 30% of the pages are assigned. I'll calculate 30% of 120.The remaining pages will be assigned to low priority. To find this, I'll subtract the number of high and medium priority pages from the total number of pages.
question：Vijay is a casual Marathi filmgoer who loves films that combine humor and great storytelling. Last month, he decided to watch a series of Marathi comedy films. Each ticket cost him ₹150. He watched 3 films in the first week and found them so hilarious that he decided to watch 4 more in the second week. In the third week, he watched 2 films but got a special discount of ₹30 on each ticket. How much money did Vijay spend in total on watching Marathi comedy films over the three weeks?
answer：First, I need to calculate the total number of films Vijay watched each week. In the first week, he watched 3 films, and in the second week, he watched 4 films. That's a total of 7 films in the first two weeks.In the third week, he watched 2 films but received a discount of ₹30 on each ticket. So, the cost per ticket in the third week was ₹150 minus ₹30, which equals ₹120.Now, I'll calculate the total cost for each week. For the first two weeks, each ticket cost ₹150, so the total cost is 7 films multiplied by ₹150, which equals ₹1050.For the third week, with the discounted price of ₹120 per ticket, the cost is 2 films multiplied by ₹120, totaling ₹240.Finally, I'll add the costs from all three weeks together: ₹1050 plus ₹240 equals ₹1290. Therefore, Vijay spent a total of ₹1290 on watching Marathi comedy films over the three weeks.
question：Professor Smith is reviewing a batch of research papers submitted by her students. She needs to ensure that each paper adheres to the required formatting and structure. Each paper takes her 15 minutes to review for formatting and an additional 10 minutes to check the structure. If Professor Smith has 8 research papers to review and she schedules 2 hours and 30 minutes in her day for this task, how many minutes will she have left after reviewing all the papers?
answer：First, I need to determine the total time Professor Smith spends reviewing one research paper. She spends 15 minutes on formatting and 10 minutes on structure, which adds up to 25 minutes per paper.Next, I'll calculate the total time required to review all 8 papers. Multiplying the time per paper by the number of papers gives 25 minutes multiplied by 8, which equals 200 minutes.Then, I'll convert the scheduled time from hours to minutes. Professor Smith has allocated 2 hours and 30 minutes, which is 150 minutes.Finally, I'll find out how much time she will have left by subtracting the total review time from the scheduled time. Subtracting 200 minutes from 150 minutes results in a negative value, indicating that Professor Smith does not have enough time to review all the papers within her scheduled time.
question：An actor named Alex is known for being quite forgetful during rehearsals, often needing reminders for his lines and stage directions. For a new play, Alex has to remember 5 different cues and 3 stage directions for each of the 4 acts in the play. However, during the first two rehearsals, he forgets 2 cues and 1 stage direction per act. If Alex attends 3 rehearsals in total, and each time he improves by remembering 1 more cue and 1 more stage direction per act than the previous rehearsal, how many cues and stage directions does he remember by the third rehearsal in total for all 4 acts?
answer：First, I need to understand the total number of cues and stage directions Alex has to remember. He has 5 cues and 3 stage directions for each of the 4 acts, which totals 20 cues and 12 stage directions.During the first two rehearsals, Alex forgets 2 cues and 1 stage direction per act. This means he remembers 3 cues and 2 stage directions per act in the first two rehearsals. For 4 acts, that's 12 cues and 8 stage directions remembered each of the first two rehearsals.In the third rehearsal, Alex improves by remembering 1 more cue and 1 more stage direction per act than the previous rehearsal. So, he remembers 4 cues and 3 stage directions per act in the third rehearsal, totaling 16 cues and 12 stage directions for all 4 acts.Finally, to find the total number of cues and stage directions Alex remembers by the third rehearsal, I add up what he remembered in each of the three rehearsals: 12 + 12 + 16 for cues, and 8 + 8 + 12 for stage directions.
question：A materials engineer is developing a new synthetic fabric for sportswear that is both lightweight and durable. The engineer needs to produce 500 square meters of this fabric. Each square meter of fabric requires 200 grams of a special polymer blend. If the engineer orders the polymer blend in batches of 10 kilograms each, how many batches does the engineer need to order to produce the 500 square meters of fabric?
answer：First, I need to determine the total amount of polymer blend required to produce 500 square meters of fabric. Each square meter requires 200 grams of the polymer blend.Next, I'll calculate the total grams needed by multiplying the number of square meters by the grams per square meter:500 square meters * 200 grams/square meter = 100,000 grams.Since the polymer blend is ordered in kilograms, I'll convert the total grams to kilograms:100,000 grams / 1,000 = 100 kilograms.Each batch contains 10 kilograms of polymer blend. To find out how many batches are needed, I'll divide the total kilograms by the batch size:100 kilograms / 10 kilograms/batch = 10 batches.Therefore, the engineer needs to order 10 batches of the polymer blend.