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question:Alex is a versatile stage performer known for his roles in both musicals and dramas. Last month, he performed in a total of 20 shows. Each musical performance lasted 2 hours, while each drama performance lasted 3 hours. If Alex spent a total of 50 hours on stage last month, how many musicals and how many dramas did he perform?
answer:To solve this problem, we need to determine how many musical performances and how many drama performances Alex did last month.Let's define:- ( x ) as the number of musical performances.- ( y ) as the number of drama performances.We have two pieces of information from the problem:1. The total number of performances (musicals and dramas) is 20. [ x + y = 20 ]2. The total time spent on stage is 50 hours. [ 2x + 3y = 50 ]We now have a system of two linear equations:1. ( x + y = 20 )2. ( 2x + 3y = 50 )Let's solve this system step by step.Step 1: Solve the first equation for one variable.From equation (1):[x + y = 20]We can express ( y ) in terms of ( x ):[y = 20 - x]Step 2: Substitute ( y = 20 - x ) into the second equation.Substitute into equation (2):[2x + 3(20 - x) = 50]Step 3: Simplify and solve for ( x ).Distribute the 3:[2x + 60 - 3x = 50]Combine like terms:[- x + 60 = 50]Subtract 60 from both sides:[-x = -10]Multiply by -1:[x = 10]Step 4: Use the value of ( x ) to find ( y ).Substitute ( x = 10 ) back into the expression for ( y ):[y = 20 - x = 20 - 10 = 10]Therefore:- Alex performed 10 musical performances.- Alex performed 10 drama performances.Now, let's write the final answer.# 10 musicals, 10 dramas
question:Coach Thompson is an Australian track and field coach who is very proud of his country's athletes. He is planning a special training day for his team. He has 15 athletes in his team, and he wants to organize them into groups for relay races. Each relay team should have 4 athletes. 1. How many complete relay teams can Coach Thompson form with his athletes?2. How many athletes will not be assigned to a relay team after forming the groups?Calculate the total number of complete teams and the number of leftover athletes.
answer:To solve the problem, we need to determine how many complete relay teams of 4 athletes each can be formed from a total of 15 athletes, and how many athletes will remain unassigned to a team after forming these groups. Step-by-Step Solution:1. Determine the number of complete teams: - Each relay team requires 4 athletes. - To find the number of complete teams, we divide the total number of athletes by the number of athletes per team. - Perform the division: ( frac{15}{4} ). - The quotient of this division will give us the number of complete teams. The quotient is 3 with a remainder, since ( 15 div 4 = 3 ) with a remainder of 3.2. Calculate the number of leftover athletes: - The remainder from the division gives us the number of athletes who will not be assigned to a complete relay team. - Therefore, the remainder is 3. Final Answer:Now, let's present the answer clearly:1. Number of complete relay teams: 32. Number of leftover athletes: 3#
question:The editor-in-chief of a fashion magazine, named Alex, is planning to feature four emerging designers in the upcoming issue. Each designer will have a 2-page spread. To increase the magazine's appeal, Alex decides to add an extra page to each designer's section to showcase a special trend prediction article. If the magazine has 120 pages in total, and 30 pages are reserved for advertisements and regular magazine sections, how many pages will be left for other fashion articles after including the sections for the four designers?
answer:To solve the problem, let's break it down step-by-step:1. Determine the total number of pages available for the designers' sections: - Each designer originally gets a 2-page spread. - An additional page is added for a special trend prediction article for each designer. Therefore, each designer's section will now be: [ 2 text{ pages} + 1 text{ page} = 3 text{ pages} ]2. Calculate the total number of pages used by all four designers: Since there are four designers, the total number of pages they will use is: [ 4 text{ designers} times 3 text{ pages/designer} = 12 text{ pages} ]3. Determine the total number of pages reserved for advertisements and regular sections: It is given that 30 pages are reserved for advertisements and regular magazine sections.4. Calculate the total number of pages used for designers, ads, and regular sections: Combine the pages used by designers and the pages reserved for ads and regular sections: [ 12 text{ pages (designers)} + 30 text{ pages (ads and regular)} = 42 text{ pages} ]5. Determine the total number of pages available for the entire magazine: It is given that the magazine has a total of 120 pages.6. Calculate the number of pages left for other fashion articles: Subtract the total pages used for designers, ads, and regular sections from the total pages of the magazine: [ 120 text{ total pages} - 42 text{ pages (designers, ads, regular)} = 78 text{ pages} ]Thus, the number of pages left for other fashion articles is 78.# 78
question:Maria is a proud Dutch soccer mom who has three children: Johan, Anika, and Pieter. Every Saturday, she takes her kids to soccer practice. Johan's practice lasts for 90 minutes, Anika's for 75 minutes, and Pieter's for 60 minutes. After practice, Maria takes them all for a special Dutch treat, stroopwafels, at a local bakery. Each stroopwafel costs 2 euros, and Maria buys 2 for each child and 1 for herself. How much time in total does Maria spend at soccer practice with her children, and how much does she spend on stroopwafels?
answer:To solve the problem, we need to find two things: the total time Maria spends at soccer practice and the total cost of stroopwafels.Step 1: Calculate the total time spent at soccer practice.Maria has to stay for the entire duration of each child's practice. Since each child's practice occurs separately, we add up the duration of each practice:- Johan's practice: 90 minutes- Anika's practice: 75 minutes- Pieter's practice: 60 minutesTotal time spent at practice = Johan's time + Anika's time + Pieter's timeTotal time = 90 minutes + 75 minutes + 60 minutes = 225 minutesStep 2: Calculate the total cost of stroopwafels.Maria buys stroopwafels for each child and herself. Each child gets 2 stroopwafels, and Maria gets 1.- Number of stroopwafels for Johan = 2- Number of stroopwafels for Anika = 2- Number of stroopwafels for Pieter = 2- Number of stroopwafels for Maria = 1Total number of stroopwafels = 2 (Johan) + 2 (Anika) + 2 (Pieter) + 1 (Maria) = 7 stroopwafelsEach stroopwafel costs 2 euros, so the total cost is:Total cost = 7 stroopwafels × 2 euros/stroopwafel = 14 eurosFinal Answer:#Total time spent at practice: 225 minutesTotal cost of stroopwafels: 14 euros#
question:The rookie quarterback, Sam, is working on overcoming his performance anxiety by focusing on his practice routine. In a week, he practices throwing passes for 5 days, and each day he throws 24 short passes, 18 medium passes, and 12 long passes. To help manage his anxiety, his coach suggests he reduces the number of passes by 10% in the second week. How many total passes will Sam throw in the second week?
answer:To solve this problem, we need to determine how many total passes Sam throws in the first week and then calculate 10% reduction for the second week.Step 1: Calculate total passes thrown in one day during the first week.- Short passes per day: 24- Medium passes per day: 18- Long passes per day: 12Total passes per day = Short passes + Medium passes + Long passes[24 + 18 + 12 = 54 text{ passes per day}]Step 2: Calculate total passes thrown in the first week.Sam practices for 5 days in a week.Total passes in the first week = Total passes per day (times) Number of practice days[54 times 5 = 270 text{ passes in the first week}]Step 3: Calculate the number of passes in the second week after a 10% reduction.First, calculate 10% of the total passes from the first week.10% of 270 = (0.10 times 270 = 27)Next, subtract this amount from the total passes in the first week to get the total passes for the second week.Total passes in the second week = Total passes in the first week - 10% reduction[270 - 27 = 243 text{ passes in the second week}]# 243
question:An internet troll named Alex has decided to test their cybersecurity skills by attempting to crack a series of passwords. Each password can be cracked based on the number of combinations Alex tries. The first password took 8 attempts to crack, the second took 12 attempts, and the third took 5 fewer attempts than the second one.If Alex continues with this pattern and the next password takes 3 times as many attempts as the first password, how many total attempts has Alex made to crack all four passwords?
answer:To solve the problem, we need to determine the number of attempts Alex made to crack each of the four passwords and then sum these attempts.1. First Password: - Alex took 8 attempts to crack the first password.2. Second Password: - Alex took 12 attempts to crack the second password.3. Third Password: - The problem states that the third password took 5 fewer attempts than the second one. - Therefore, the third password took (12 - 5 = 7) attempts.4. Fourth Password: - The fourth password took 3 times as many attempts as the first password. - Therefore, the fourth password took (3 times 8 = 24) attempts.Next, we sum up all the attempts for the four passwords:- Attempts for the first password: 8- Attempts for the second password: 12- Attempts for the third password: 7- Attempts for the fourth password: 24Total attempts = (8 + 12 + 7 + 24).Let's calculate the total:- (8 + 12 = 20)- (20 + 7 = 27)- (27 + 24 = 51)Thus, Alex made a total of 51 attempts to crack all four passwords.Final Answer:# 51