answer:Let's first determine Rachel's rate of stuffing envelopes per hour. In the first hour, Rachel stuffs x envelopes. So the total number of envelopes stuffed by the end of the second hour is x + 141. Given that Rachel has 8 hours to complete the task, she needs to stuff 1,500 envelopes in total. We can write a simple equation to solve for x: Rachel's total number of envelopes stuffed in 8 hours = 1,500 envelopes x (envelopes per hour) + 141 + x (envelopes per hour) = 1,500 envelopes 2x + 141 = 1,500 Now, we can solve for x: 2x = 1,500 - 141 = 1,359 x = 1,359 / 2 = 679.5 Since Rachel needs to stuff whole envelopes per hour, we round x down to get the nearest whole number: x = 679 So, the value of x is 679. However, you said the answer is 204, which is not consistent with the given information and the calculation we just performed. Please recheck the information provided., If Rachel needs to stuff 204 envelopes per hour to finish the job in 8 hours, then the total number of envelopes she needs to stuff is: 204 envelopes/hour × 8 hours = 1,632 envelopes However, there are only 1,500 envelopes in total. This means that Rachel will not be able to finish the job in 8 hours if she stuffs 204 envelopes per hour. As for the value of x, the problem states that Rachel stuffs x envelopes in the first hour and 141 envelopes in the second hour. Since we do not have enough information to determine the value of x, it cannot be determined at this time.,Rachel has eight hours to complete the task, and there are 1,500 envelopes. In the first hour, Rachel stuffs x envelopes. In the second hour, Rachel stuffs 141 envelopes. To find out how many envelopes Rachel needs to stuff per hour to finish the job, we can subtract the number of envelopes stuffed in the first and second hour from the total number of envelopes. The total number of envelopes stuffed in the first and second hour is x + 141. The number of envelopes left to stuff is 1,500 - (x + 141). Since Rachel has eight hours to complete the task, we can divide the number of envelopes left to stuff by the number of hours remaining: (1,500 - (x + 141)) / 6. We are given that Rachel needs to stuff 204 envelopes per hour to finish the job, so we can write: (1,500 - (x + 141)) / 6 = 204. Simplifying the left side, we get: (1,359 - x) / 6 = 204. Multiplying both sides by 6, we get: 1,359 - x = 1,224. Subtracting 1,359 from both sides, we get: -x = -135. Multiplying both sides by -1, we get: x = 135. The value of x is 135. 135 The answer is: 135

answer:Roland has a 12cm long thread. His teacher says he needs an additional three-quarters of what he has, which is 3/4 * 12cm = 9cm. So, he needs a total of 12cm (existing thread) + 9cm (additional thread) = 21cm of thread to complete the exercise.,Roland has a 12cm long thread. His teacher says he needs an additional three-quarters of what he has, which is 3/4 x 12cm = 9cm. Therefore, the total length required is 12cm + 9cm = 21cm. 21 The answer is: 21, First, we need to find out the additional length of thread that Roland needs. We know that his teacher asked for three-quarters of what Roland already has. So, we calculate: Additional length = Three-quarters of 12cm = (3/4) * 12cm = 9cm Now, to find the total length required, we need to add the additional length to the length Roland already has: Total length = Initial length + Additional length = 12cm + 9cm = 21cm So, Roland needs a total length of 21cm to complete his exercise.

answer:To solve this problem, we need to determine the value of x, which represents the number of marks fewer than the first ten students scored by the next 15 students. Let's break down the information given: Total number of students in Kylie's class: 50 Number of students who scored 90 marks: 10 Number of students who scored x marks fewer than the first ten students: 15 Number of students who scored 60 marks: 50 - (10 + 15) = 25 Average marks for the whole class: 72 We can set up the equation as follows: (10 * 90) + (15 * (90 - x)) + (25 * 60) = (50 * 72) Let's simplify and solve for x: 900 + (15 * (90 - x)) + 1500 = 3600 900 + 1350 - 15x + 1500 = 3600 3750 - 15x = 3600 To isolate x, we subtract 3750 from both sides of the equation: 3750 - 3750 - 15x = 3600 - 3750 -15x = -150 Finally, we divide both sides of the equation by -15 to solve for x: x = -150 / -15 x = 10 The value of x is 10. 10 The answer is: 10,To solve this problem, we need to determine the value of x, which represents the difference in marks between the first ten students and the next fifteen students. Let's break down the information given: Number of students in the class: 50 Number of students with 90 marks: 10 Number of students with x marks fewer than the first ten: 15 Number of students with 60 marks each: 50 (since the number of students with 90 and x marks fewer is constant, the rest must be 60 marks each) Average marks for the whole class: 72 We can set up the equation as follows: (Number of students with 90 marks * 90 + Number of students with x marks fewer * (90 - x) + Number of students with 60 marks * 60) / Total number of students = Average marks for the whole class (10 * 90 + 15 * (90 - x) + 50 * 60) / 50 = 72 Now, we can simplify and solve for x: 900 + 1350 - 15x + 3000 = 3600 + 72x 3900 - 15x = 3600 + 72x 3900 - 3600 = 72x + 15x 300 = 87x Now, divide both sides by 87 to find the value of x: 300 / 87 = 3.457 (approximately) Therefore, the value of x is approximately 3.457., The value of x is 75. Here's the reasoning: 1. We know that there are 50 students in the class, and ten of them scored 90 marks. 2. This means that there are 40 students who didn't score 90 marks (50 - 10 = 40). 3. Fifteen students scored x marks fewer than the first ten students, so these 15 students scored (90 - x) marks. 4. The remaining students (50 - 10 - 15 = 25) scored 60 marks each. 5. Now let's calculate the total marks scored by all the students: 10 * 90 + 15 * (90 - x) + 25 * 60. 6. To find the average marks for the whole class, we'll divide this total by 50 (the number of students). So, the equation becomes: (10 * 90 + 15 * (90 - x) + 25 * 60) / 50 = 72. 7. Solving for x, we first multiply everything out: 900 + 1350 - 15x + 1500 = 3600. 8. Next, we simplify the equation: -15x = -375. 9. Finally, we solve for x: x = 375 / 15 = 25. However, upon re-evaluating the problem, I realized I made an error in my initial solution. The correct calculation should be as follows: 1. The total marks of the 15 students who scored x marks less than the top 10 should be 15x. 2. Therefore, the total marks equation becomes: 900 + 15x + 1500 = 3600 (the same as before). 3. Solving for x again, we have: 15x = 1200, so x = 80. 4. But this value doesn't make sense in the context of the problem because it would mean that the 15 students scored higher than the first ten students, which contradicts the given information. 5. So, let's reconsider the possibility that the remaining 25 students scored an average of 60 marks. Instead, they might have scored the same number of marks, let's call it y. 6. Now, the total marks equation becomes: 900 + 15(90 - x) + 25y = 50y. 7. Solving for y, we get: 900 + 1350 - 15x = 25y - 1350, so 25y = 2700 + 15x. 8. Since the first ten students scored 90 marks each, then 15x represents the combined score of the 15 students who scored less than the first ten. Thus, 15x <= 1350 (as the maximum score for these 15 students would be if they all scored 90 - x). 9. Using this information, we can find upper bounds for x. For example, if x = 75, then 15x = 1125, which is still less than 1350. 10. With x = 75, our total marks equation becomes: 25y = 2700 + 1125 = 3825, so y = 153. 11. Since y represents the number of marks scored by the remaining 25 students, this value is reasonable because it falls within the range of possible scores (60 to 90). 12. Therefore, the correct value of x is 75, making the final equation: 900 + 15(90 - 75) + 25 * 60 = 50 * 72.

answer:Samuel drives 50 miles/hour for 3 hours, which is a total distance of 50 * 3 = 150 miles. Then, he speeds up to 80 miles/hour for 4 hours, which is a total distance of 80 * 4 = 320 miles. In total, Samuel has driven 150 + 320 = 470 miles. Since he needs to travel 600 miles to reach the hotel, he is still 600 - 470 = 130 miles away from the hotel.,In the first 3 hours, Samuel travels 50 miles/hour * 3 hours = 150 miles. In the next 4 hours, Samuel travels 80 miles/hour * 4 hours = 320 miles. So in total, Samuel has traveled 150 miles + 320 miles = 470 miles. Since he needs to travel 600 miles to the hotel, he is 600 miles - 470 miles = 130 miles away from the hotel. 130 The answer is: 130, Samuel has traveled 50 miles/hour * 3 hours + 80 miles/hour * 4 hours = 150 miles + 320 miles = 470 miles. Therefore, Samuel is 600 miles - 470 miles = 130 miles away from the hotel. Answer: boxed{130}.