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question：Emily is trying to manage the rodents in her farm. Each cat she brings in catches 5 mice, and each time she sets traps she reduces the total mouse population to 75% of what it was previously. If the farm has 600 mice to start, and Emily sets traps once and brings in 15 cats, how many mice are left?
answer：First, I need to determine the initial number of mice on Emily's farm, which is 600.Emily sets traps once, reducing the mouse population to 75% of its current number. To calculate this, I multiply 600 by 0.75, resulting in 450 mice remaining after the traps are set.Next, Emily brings in 15 cats. Each cat catches 5 mice, so the total number of mice caught by the cats is 15 multiplied by 5, which equals 75 mice.Finally, I subtract the number of mice caught by the cats from the number of mice remaining after the traps were set. This means subtracting 75 from 450, which leaves 375 mice on the farm.
question：Emily takes 2 days off from tutoring per week. On the days she does tutor, she tutors for 3 hours at a time and makes 15 an hour. How much does she make a week?
answer：First, I need to determine how many days Emily tutors each week. Since she takes 2 days off, she tutors on 5 days.Next, I'll calculate the total number of hours she tutors weekly. She tutors for 3 hours each day, so 5 days multiplied by 3 hours equals 15 hours.Finally, I'll find out her weekly earnings by multiplying the total hours by her hourly rate. At 15 per hour, 15 hours multiplied by 15 equals 225.
question：Joseph gave 23 cards to each of his 15 students and had 12 cards left. How many cards did Joseph have at first?
answer：First, I need to determine the total number of cards Joseph distributed to his students. He gave 23 cards to each of his 15 students.Next, I'll calculate the total number of cards distributed by multiplying the number of cards per student by the number of students:23 cards/student × 15 students = 345 cards.After distributing the cards, Joseph had 12 cards left. To find out how many cards he had initially, I'll add the cards he distributed to the cards he had remaining:345 cards + 12 cards = 357 cards.Therefore, Joseph initially had 357 cards.
question：Iris’ family is planning a surprise birthday party for her. The party will include her 3 uncles and 4 aunts who have a son and daughter each as well as her brother and mother. In total, how many people are coming to Iris’ birthday party?
answer：First, I identify all the family members mentioned in the problem.Iris has 3 uncles and 4 aunts, making a total of 7 aunts and uncles.Each of these 7 aunts and uncles has a son and a daughter, which adds 2 children per aunt or uncle. Therefore, there are 7 multiplied by 2, resulting in 14 nieces and nephews.Additionally, Iris has a brother and a mother, adding 2 more family members.Including Iris herself, the total number of people attending the party is 1 (Iris) + 7 (aunts and uncles) + 14 (nieces and nephews) + 2 (brother and mother) = 24 people.
question：Emily works 6 hours a day, 4 days a week, 3 weeks a month as a part-time employee. Her colleague, Ryan, is a student intern and works 1 hour less than Emily every day. Emily earns 12 an hour, and Ryan earns a third of that amount. What is the total amount the company pays for both Emily and Ryan in one month?
answer：First, I need to calculate the number of hours Emily works each month. She works 6 hours a day, 4 days a week, and for 3 weeks. So, her total monthly hours are 6 multiplied by 4, then by 3, which equals 72 hours.Next, I'll determine Ryan's daily working hours. Since he works 1 hour less than Emily each day, he works 5 hours per day. Over the same 4 days a week and 3 weeks, Ryan's total monthly hours are 5 multiplied by 4, then by 3, totaling 60 hours.Emily earns 12 per hour, so her monthly earnings are 72 hours multiplied by 12, which equals 864. Ryan earns a third of Emily's hourly rate, so his hourly wage is 4. His monthly earnings are 60 hours multiplied by 4, totaling 240.Finally, to find the total amount the company pays both Emily and Ryan in one month, I'll add their monthly earnings together: 864 plus 240 equals 1,104.
question：Emily has 6 raffle tickets to sell. She sells the first ticket for 2. She then sells each successive ticket for a dollar more than the previous ticket. She plans to keep a 6 profit and give the remaining money as the prize. How much money will the winner of the raffle receive?
answer：First, Emily sells the first ticket for 2. Each subsequent ticket is sold for 1 more than the previous one. Since she has 6 tickets to sell, the selling prices for each ticket are 2, 3, 4, 5, 6, and 7.Next, I'll calculate the total revenue from selling all 6 tickets by summing these amounts: 2 + 3 + 4 + 5 + 6 + 7, which equals 27.Emily plans to keep a 6 profit from the total revenue. To find out how much money will be given as the prize, I'll subtract her profit from the total revenue: 27 - 6 = 21.Therefore, the winner of the raffle will receive 21.