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question：Jamie is a marketing manager for a food company that makes different types of snacks. She recently conducted a survey to gather honest feedback from customers about three new snack products: crunchy chips, chewy granola bars, and spicy popcorn. She received feedback from 120 people in total. 40 people gave feedback on the crunchy chips, 35 people reviewed the chewy granola bars, and the remaining people reviewed the spicy popcorn. How many people gave feedback on the spicy popcorn?
answer：First, I need to determine the total number of people who provided feedback on all three snack products. Jamie received feedback from 120 people in total.Next, I'll add the number of people who reviewed the crunchy chips and the chewy granola bars. There were 40 people who reviewed the crunchy chips and 35 people who reviewed the chewy granola bars. Adding these together gives 75 people.Finally, to find out how many people reviewed the spicy popcorn, I'll subtract the number of people who reviewed the first two products from the total number of respondents. So, 120 total people minus 75 people equals 45 people who gave feedback on the spicy popcorn.
question：Alex is a software engineer who has worked remotely for most of his career. On average, he spends 6 hours a day coding, 1.5 hours in virtual meetings, and 1 hour on emails and other tasks. If Alex works 5 days a week, how many hours does he spend on each activity per week? Also, calculate the total number of hours Alex works per week.
answer：First, I need to determine how many hours Alex spends on each activity per week. He works 5 days a week, so I'll multiply the daily hours for each activity by 5.For coding, Alex spends 6 hours each day. Multiplying 6 hours by 5 days gives 30 hours per week.Next, for virtual meetings, he spends 1.5 hours each day. Multiplying 1.5 hours by 5 days results in 7.5 hours per week.Lastly, for emails and other tasks, he spends 1 hour each day. Multiplying 1 hour by 5 days equals 5 hours per week.To find the total number of hours Alex works per week, I'll add up the hours from all activities: 30 hours (coding) + 7.5 hours (meetings) + 5 hours (emails and tasks) equals 42.5 hours per week.
question：A young novice DJ named Sam is creating a new playlist for their next event. Initially, Sam is unsure about including classic rock tracks in their modern sets. However, after some encouragement, Sam decides to add a mix of classic rock and modern songs. Sam plans to play a total of 30 songs. For every 3 modern songs, Sam includes 2 classic rock songs. How many classic rock songs will Sam include in the playlist?
answer：First, I need to determine the ratio of modern songs to classic rock songs in Sam's playlist. According to the problem, for every 3 modern songs, Sam includes 2 classic rock songs. This gives a ratio of 3:2.Next, I'll define variables to represent the number of modern and classic rock songs. Let ( 3x ) represent the number of modern songs and ( 2x ) represent the number of classic rock songs.The total number of songs in the playlist is 30. Therefore, I can set up the equation:[3x + 2x = 30]Combining like terms, this simplifies to:[5x = 30]Solving for ( x ), I divide both sides by 5:[x = 6]Now, I'll calculate the number of classic rock songs by substituting ( x = 6 ) into ( 2x ):[2x = 2 times 6 = 12]So, Sam will include 12 classic rock songs in the playlist.
question：Alex is a sedentary office worker who enjoys watching extreme sports and travel vlogs after work. One day, Alex watched a series of vlogs that covered different activities in various countries. The first vlog was about skiing in Switzerland and lasted 15 minutes. The second vlog was about surfing in Hawaii and lasted twice as long as the first one. The third vlog was about rock climbing in Australia and lasted 10 minutes longer than the surfing vlog. If Alex watched all three vlogs consecutively, how many total minutes did Alex spend watching these vlogs?
answer：First, I identify the duration of each vlog. The skiing vlog in Switzerland is 15 minutes long.Next, the surfing vlog in Hawaii lasts twice as long as the skiing vlog. So, 2 multiplied by 15 minutes equals 30 minutes.Then, the rock climbing vlog in Australia is 10 minutes longer than the surfing vlog. Adding 10 minutes to the 30 minutes of the surfing vlog gives 40 minutes.Finally, to find the total time Alex spent watching all three vlogs, I add up the durations: 15 minutes (skiing) + 30 minutes (surfing) + 40 minutes (rock climbing) equals 85 minutes.
question：An undergraduate physics student studying astrophysics is observing a binary star system. In this system, one star is a red giant and the other is a white dwarf. The red giant completes an orbit around the common center of mass every 50 days, and the white dwarf completes its orbit every 25 days. If both stars start at the same point in their orbit today, how many days will it take for them to be at the same point in their orbit again?
answer：First, I need to determine how many days it will take for both the red giant and the white dwarf to return to the same starting point in their orbits simultaneously.The red giant completes an orbit every 50 days, and the white dwarf completes an orbit every 25 days. To find when they will align again, I should calculate the least common multiple (LCM) of their orbital periods.The LCM of 50 and 25 is 50 days. This means that after 50 days, both stars will have completed an integer number of orbits and will be back at the starting point together.Therefore, it will take 50 days for both stars to be at the same point in their orbit again.
question：Officer Jordan, a dedicated corrections officer, has been working on a new initiative to encourage positive change among the inmates. She decided to start a book club and personally donated 15 books to get it started. After noticing the inmates' enthusiasm, another five officers donated 8 books each. The library already had 42 books before any donations. Officer Jordan wants to ensure there is at least one book for each of the 60 inmates in the facility. How many more books, if any, are needed to have at least one book per inmate?
answer：First, I need to calculate the total number of books donated by Officer Jordan and the other officers. Officer Jordan donated 15 books, and each of the five officers donated 8 books, which totals 40 books. Adding these together, there are 55 donated books.Next, I'll add the donated books to the existing library collection. The library already had 42 books, so combining that with the 55 donated books gives a total of 97 books.Finally, I need to determine if there are enough books for each of the 60 inmates. Since there are 97 books available and only 60 inmates, there are more than enough books. Therefore, no additional books are needed.