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question:An experienced traditional artist named Alex is organizing an art challenge for local students. To maintain a positive atmosphere, Alex decides to give out art supply kits as rewards to all participants. Alex has 5 boxes of watercolor sets, each containing 12 sets. Additionally, Alex has 8 packs of sketch pencils, with each pack containing 10 pencils. For each participant, Alex wants to give 1 watercolor set and 2 sketch pencils.If there are 15 students participating in the art challenge, how many watercolor sets and sketch pencils will Alex have left after preparing the rewards for all participants?
answer:To solve the problem, we need to determine how many watercolor sets and sketch pencils Alex will have left after preparing rewards for all 15 students. Step 1: Calculate the Total Number of Watercolor Sets and Sketch Pencils1. Total Watercolor Sets: - Alex has 5 boxes of watercolor sets. - Each box contains 12 sets. - Total watercolor sets = 5 boxes × 12 sets/box = 60 sets.2. Total Sketch Pencils: - Alex has 8 packs of sketch pencils. - Each pack contains 10 pencils. - Total sketch pencils = 8 packs × 10 pencils/pack = 80 pencils. Step 2: Determine the Total Number of Watercolor Sets and Sketch Pencils Needed for the Participants1. Watercolor Sets Needed: - Each participant receives 1 watercolor set. - For 15 students: 15 students × 1 set/student = 15 sets needed.2. Sketch Pencils Needed: - Each participant receives 2 sketch pencils. - For 15 students: 15 students × 2 pencils/student = 30 pencils needed. Step 3: Calculate the Remaining Watercolor Sets and Sketch Pencils1. Remaining Watercolor Sets: - Alex starts with 60 sets. - Alex gives out 15 sets. - Remaining sets = 60 sets - 15 sets = 45 sets.2. Remaining Sketch Pencils: - Alex starts with 80 pencils. - Alex gives out 30 pencils. - Remaining pencils = 80 pencils - 30 pencils = 50 pencils. Final AnswerAfter preparing rewards for all participants, Alex will have:# 45 watercolor sets and 50 sketch pencils left.
question:Alex is a software engineer who loves to play around with LED lights. He is working on a project to create a colorful LED display for his home office. Alex has a total of 150 LED lights, and he wants to arrange them in a pattern that repeats every 15 lights. In each pattern, he uses 5 red lights, 3 blue lights, 4 green lights, and the rest are yellow lights. How many yellow LED lights will Alex use in his entire display?
answer:To solve this problem, we need to determine how many yellow LED lights Alex uses in his entire display. Let's follow the steps below:1. Determine the composition of one pattern: - Alex has a pattern of 15 lights. - In each pattern, he uses: - 5 red lights - 3 blue lights - 4 green lights2. Calculate the number of yellow lights per pattern: - Total lights per pattern = 15 - Total non-yellow lights per pattern = 5 (red) + 3 (blue) + 4 (green) = 12 - Therefore, yellow lights per pattern = 15 - 12 = 33. Determine how many complete patterns are in the entire display: - Alex has a total of 150 LED lights. - The number of complete 15-light patterns he can create = ( frac{150}{15} = 10 )4. Calculate the total number of yellow lights used: - Yellow lights per pattern = 3 - Total number of patterns = 10 - Total yellow lights = 3 yellow lights per pattern * 10 patterns = 30 yellow lightsThus, Alex will use a total of 30 yellow LED lights in his entire display.Now, output the final answer:# 30
question:Ms. Sarah, a high school teacher who prefers traditional methods over technology, decided to conduct an experiment with her students to understand the impact of technology on learning. She divided her class of 30 students into two groups. In one group, 18 students used textbooks and paper for a week, while in the other group, 12 students used tablets and educational apps. At the end of the week, she gave a quiz to both groups. The textbook group scored an average of 75 points, and the tablet group scored an average of 82 points. Calculate the total number of points scored by each group and find the difference in total points between the two groups.
answer:To solve the problem, we need to calculate the total number of points scored by each group and then find the difference in total points between the two groups.Step 1: Calculate the total points for the textbook group.The textbook group consists of 18 students, and their average score is 75 points. To find the total points scored by this group, we multiply the number of students by the average score:[text{Total points for textbook group} = 18 times 75 = 1350]Step 2: Calculate the total points for the tablet group.The tablet group consists of 12 students, and their average score is 82 points. To find the total points scored by this group, we multiply the number of students by the average score:[text{Total points for tablet group} = 12 times 82 = 984]Step 3: Calculate the difference in total points between the two groups.Now, subtract the total points of the tablet group from the total points of the textbook group to find the difference:[text{Difference} = 1350 - 984 = 366]The difference in total points between the textbook group and the tablet group is 366 points.# 366
question:Alex is a professional athlete who believes in natural bodybuilding and emphasizes the importance of a balanced diet and regular exercise. He plans his meals carefully to consume 150 grams of protein each day. On Monday, he had a protein shake with 30 grams of protein, a chicken breast with 50 grams of protein, and a serving of almonds with 10 grams of protein. For dinner, he had a salmon fillet that provided the rest of his daily protein intake. How many grams of protein did the salmon fillet provide?
answer:To solve the problem, we need to determine how many grams of protein Alex's salmon fillet provided.1. Determine the total protein Alex needs: - Alex needs 150 grams of protein each day.2. Calculate the protein intake from other sources: - Protein from the shake: 30 grams - Protein from the chicken breast: 50 grams - Protein from almonds: 10 grams3. Add the protein from the shake, chicken breast, and almonds: [ 30 text{ grams (shake)} + 50 text{ grams (chicken breast)} + 10 text{ grams (almonds)} = 90 text{ grams} ]4. Calculate the remaining protein requirement: - To find out how much protein the salmon fillet provided, subtract the total protein consumed from other sources from the daily requirement: [ 150 text{ grams (daily requirement)} - 90 text{ grams (from other sources)} = 60 text{ grams} ]The salmon fillet provided 60 grams of protein.# 60
question:Jonathan, a British atheist who questions everything related to religion, recently read a book discussing the historical construction of various cathedrals around the world. He was particularly intrigued by the architectural details, so he decided to explore further. He found that the total height of a cathedral's spire is made up of three different sections. The base section is 25 meters tall, the middle section is twice as tall as the base section, and the top section is 5 meters less than the middle section. What is the total height of the spire?
answer:To solve this problem, we need to calculate the height of each section of the spire and then sum them up to get the total height.1. Base Section: The base section of the spire is given as 25 meters tall.2. Middle Section: The middle section is twice as tall as the base section. Therefore, the height of the middle section is: [ text{Middle Section Height} = 2 times text{Base Section Height} = 2 times 25 = 50 text{ meters} ]3. Top Section: The top section is 5 meters less than the middle section. Therefore, the height of the top section is: [ text{Top Section Height} = text{Middle Section Height} - 5 = 50 - 5 = 45 text{ meters} ]4. Total Height: The total height of the spire is the sum of the heights of the three sections: [ text{Total Height} = text{Base Section Height} + text{Middle Section Height} + text{Top Section Height} ] [ text{Total Height} = 25 + 50 + 45 = 120 text{ meters} ]Thus, the total height of the spire is 120 meters.# 120 meters
question:An amateur photographer named Alex loves exploring hidden gems in their city and sharing photos online. Alex visited 4 different hidden spots in one week and took pictures at each location. At the first location, Alex took 15 photos, at the second location, 18 photos, at the third location, 12 photos, and at the fourth location, 25 photos. Alex shares 3 photos from each location on their online page every day. How many days will it take Alex to share all the photos they took in that week?
answer:To solve the problem, follow these steps:1. Calculate the total number of photos taken by Alex: - At the first location, Alex took 15 photos. - At the second location, Alex took 18 photos. - At the third location, Alex took 12 photos. - At the fourth location, Alex took 25 photos. Add these numbers together to find the total: [ 15 + 18 + 12 + 25 = 70 ]2. Determine how many photos Alex shares each day: - Alex shares 3 photos from each location every day. - There are 4 locations, so Alex shares (3 times 4 = 12) photos each day.3. Calculate the number of days required to share all the photos: - Divide the total number of photos by the number of photos shared per day: [ frac{70}{12} approx 5.8333 ] Since Alex cannot share photos for a fraction of a day, we round up to the nearest whole number. Therefore, Alex will need 6 days to share all the photos.# 6