The total number of first graders and second graders in an elementary school is 330. If the number of students in the second grade is 1.2 times the number of students in the first grade, how many students are in each grade?
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The diameter of the base of a cylinder barrel is 20 inches. If it is 25 inches deep, what is the volume of the cylinder barrel?
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The diameter of one of a cylinder’s bases is 5 inches. If the cylinder is 20 inches high, what is the surface area of the cylinder?
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Granddad raises a total of 18 black rabbits and white rabbits. If the number of white rabbits is 5 times the number of black rabbits, how many of each type does Granddad have?
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The diameter of one of a cylinder’s bases is 3.2 feet. If the cylinder is 5 feet high, what is the area of the lateral surface?
Granddad raises a total of 18 black rabbits and white rabbits. If the number of black rabbits is 1/5 of the number of white rabbits, how many of each type does Granddad have?
Three ropes are 120 inches long, 90 inches long and 150 inches long. They are cut into sections with no remaining parts. If each section has the same length, what is the largest possible length for each section? How many sections can we get altogether?
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Answer to the question:
Since each section has the same length, that means we need to find the common factors of 120, 90 and 150. Since we need to find the largest possible length of each section, we need to find the greatest common factor. That is 30. So the largest possible length of each section is 30 inches.
The rope that is 120 inches long is cut into 4 sections. The rope that is 90 inches long is cut into 3 sections. The rope that is 150 inches long is cut into 5 sections. Therefore, all the ropes are cut into a total of 12 sections.
The product of two natural numbers is 420. If their greatest common factor is 12,what is their least common multiple?
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According to this rule: The product of the greatest common factor and the least common multiple of the two numbers equals to the product of the two numbers
The least common multiple of the two numbers is: 420÷12=35
Lisa and Sarah were given a word problem to work on:
The distance between City A and City B is 360 miles. A car was going at 60 miles per hour from City A to City B; on the way back, the car was going at 40 miles per hour because it was raining really hard so that driver could not see very well. What was the average speed of the car for the round trip?
This was Lisa’s answer:
(60+40)÷2=50 miles per hour
Sarah said: “No, you cannot solve the problem like that. This is how to solve it.”
This was Sarah’s answer:
The total distance for the round trip: 360×2=720 miles
The amount of time the car used to travel from City A to City B:
The amount of time the car used to travel back to City A from City B:
The total amount of time for the round trip:
The average speed for the round trip= the total distance for the round trip÷ the total amount of time spent on the round trip= 720÷15=48 miles per hour
Friends, I believe that you all think that Sarah is right and she is. Remember: when you solve a word problem on travelling, finding the average speed is not the same as finding the average age, the average height, etc.
A stick is 1 yard long. If 1/5 is cut off at first, 1/6 of the remaining section is cut off secondly, 1/7 of the last remaining section is cut off thirdly and the cutting keeps on until 1/10 of the last remaining section is cut off finally, what is the length of the remaining stick?
The solution to this type of question usually has a pattern:
When 1/5 is cut off, 4/5 yard is left;
When 1/6 of the remaining section is cut off, 5/6 of 4/5 yard is left:
4/5 yard × 5/6 =4/6 yard
When 1/7 of the last remaining section is cut off, 6/7 of 4/6 yard is left:
6/7 × 4/6 = 4/7 yard
In this pattern, when 1/10 of the last remaining part is cut off, the amount left should be:
4/10 yard= 2/5 yard ( simplest term)