2.A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A.no more than 50
B.no less than 50
C.no less than 45
D.no more than 45
3.It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
A.30 miles per hour
B.56 miles per hour
C.50 miles per hour
D.64 miles per hour
4.Raphael is timing how fast he can do a series of 5 math questions, aiming to complete them in less than 20 minutes. He has done 3 questions so far, with each of them taking 3 minutes to complete.
On average, how much time does Raphael have on each remaining question so he can reach his goal?
A.Raphael has no more than 5 minutes and 50 seconds to complete each remaining question.
B.Raphael has less than 5 minutes and 50 seconds to complete each remaining question.
C.Raphael has less than 5 minutes and 30 seconds to complete each remaining question.
D.Raphael has no more than 5 minutes and 30 seconds to complete each remaining question.
5.A retail store is buying a 500 count for a device and another 200 count for another version of the same device that costs $100 less than the original. What is the maximum cost of the original device, given that the store did not go over the budget of $155,000?
A.no more than $150
B.no more than $250
C.less than $150
D.less than $250
2. To find out how many small machines can be fit without exceeding the weight limit of the truck, we need to subtract the weight of the big machine from the weight capacity of the truck and divide the remaining weight by the weight of each small machine.
Weight capacity of the truck: 3000 pounds
Weight of the big machine: 300 pounds
Weight of each small machine: 60 pounds
Remaining weight after deducting the weight of the big machine: 3000 - 300 = 2700 pounds
To find the maximum number of small machines that can be fit, we divide the remaining weight by the weight of each small machine:
Maximum number of small machines = remaining weight / weight of each small machine
Maximum number of small machines = 2700 / 60 = 45
Therefore, the answer is D. no more than 45 can be fit without exceeding the weight limit of the truck.
3. To find the minimum speed Claude should travel in order to reach the destination in less than 48 minutes, we need to consider the additional distance traveled due to the detour.
Original time for the trip: 40 minutes
Additional distance due to detour: 8 miles
Original speed: 48 miles per hour
To find the minimum speed, we need to find the new time for the trip and then divide the additional distance by the new time.
New time for the trip = original time + additional time
Additional time = (additional distance / original speed) * 60 (to convert from hours to minutes)
New time for the trip = 40 + (8/48) * 60
New time for the trip = 40 + (0.1667) * 60
New time for the trip = 40 + 9.9999
New time for the trip = 49.9999
Since Claude needs to reach the destination in less than 48 minutes, the minimum speed he should travel is 50 miles per hour.
Therefore, the answer is C. 50 miles per hour is the minimum speed Claude should travel.
4. To find out the average time Raphael has on each remaining question to reach his goal, we need to subtract the time already spent on the questions from the total time allowed and divide it by the number of remaining questions.
Total time allowed: 20 minutes
Time spent on questions: 3 minutes x 3 questions = 9 minutes
Remaining time for questions = total time allowed - time spent on questions
Remaining time for questions = 20 - 9 = 11 minutes
Number of remaining questions = 5 - 3 = 2 questions
Average time for each remaining question = remaining time for questions / number of remaining questions
Average time for each remaining question = 11 / 2 = 5.5 minutes
Therefore, the answer is A. Raphael has no more than 5 minutes and 50 seconds to complete each remaining question.
5. Let's assume the cost of the original device is X dollars.
Cost of the 500 count for the original device = X * 500
Cost of the 200 count for the other version of the device = (X - 100) * 200
Total cost = Cost of the 500 count + Cost of the 200 count
Total cost = X * 500 + (X - 100) * 200
Given that the total cost cannot exceed $155,000:
X * 500 + (X - 100) * 200 ≤ 155,000
Simplifying the equation:
500X + 200X - 20,000 ≤ 155,000
700X ≤ 175,000
X ≤ 250
Therefore, the maximum cost of the original device is D. less than $250.
2. To solve this question, we need to determine how many small machines can be added to the pickup truck without exceeding its weight limit.
First, we calculate the weight of the machine and the smaller ones combined:
Weight of the machine = 300 pounds
Weight of each small machine = 60 pounds
Total weight = 300 pounds + (number of small machines * 60 pounds)
Since the truck's weight limit is 3000 pounds, we set up the equation:
Total weight ≤ 3000 pounds
300 + (number of small machines * 60) ≤ 3000
To find the minimum number of small machines, we solve the inequality:
(number of small machines * 60) ≤ 3000 - 300
number of small machines ≤ (3000 - 300) / 60
number of small machines ≤ 2700 / 60
number of small machines ≤ 45
Therefore, the answer is D. no more than 45 small machines.
3. To solve this question, we need to determine the minimum speed Claude should travel in order to reach his destination in less than 48 minutes, even with the longer detour.
Claude's usual time = 40 minutes
Extra time due to detour = 48 minutes - 40 minutes = 8 minutes
Extra distance traveled due to detour = 8 miles
To find the minimum speed, we calculate the speed needed to cover the extra distance in the extra time:
Speed = Extra distance / Extra time
Speed = 8 miles / 8 minutes
Speed = 1 mile/minute = 60 miles/hour
Therefore, the answer is B. 56 miles per hour.
4. To solve this question, we need to calculate the average time Raphael has for each remaining question to reach his goal.
Total time goal = 20 minutes
Total time spent on 3 questions = 3 questions * 3 minutes/question = 9 minutes
Time remaining for remaining questions = Total time goal - Total time spent
Time remaining for remaining questions = 20 minutes - 9 minutes = 11 minutes
Number of remaining questions = 5 questions - 3 questions = 2 questions
Average time Raphael has for each remaining question = Time remaining / Number of remaining questions
Average time = 11 minutes / 2 questions = 5.5 minutes per question
Therefore, the answer is A. Raphael has no more than 5 minutes and 50 seconds to complete each remaining question.
5. To solve this question, we need to find the maximum cost of the original device, given the constraints provided.
Cost of the original device = X
Cost of the second device = X - $100
Number of original devices = 500 count
Number of second devices = 200 count
Total cost = (Cost of the original device * Number of original devices) + (Cost of the second device * Number of second devices)
Total cost ≤ $155,000
[(X * 500) + ((X - $100) * 200)] ≤ $155,000
To determine the maximum cost of the original device, we solve the inequality:
(X * 500) + (X - $100) * 200 ≤ $155,000
500X + 200(X - $100) ≤ $155,000
Combine like terms:
500X + 200X - $20,000 ≤ $155,000
700X - $20,000 ≤ $155,000
700X ≤ $175,000
X ≤ $250
Therefore, the answer is D. less than $250.
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
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