39. Students are cleaning a local park in groups. There are 50 boys & 75 girls. Each group has the same number of boys and the same number of girls. What is the greatest possible number of groups?
40. You are dividing a community garden 35 m long by 15 m wide into equal sized square gardens. Find the greatest possible dimensions of each square.
Sorry, I'm just having some trouble understanding these kinds of problems :) I have three more like these after that, but I figured that if I could get some help on these then I would understand the others. Thanks. :D
Find the lowest common factor (besides just 1) of 50 and 75: 5
So, if each group has 5 boys or girls, you have 10 groups of boys and 15 groups of girls
The GCD of 15 and 35 is 5
So, make 5x5 squares. 3x7 of them.
No problem! I'm here to help. Let's break down each problem step by step:
39. To find the greatest possible number of groups, we need to find the largest common factor of 50 and 75 (which represents the maximum number of students per group).
First, let's find the factors of 50: 1, 2, 5, 10, 25, and 50.
Next, let's find the factors of 75: 1, 3, 5, 15, 25, and 75.
Looking at the lists of factors, we see that the largest common factor of 50 and 75 is 25.
Therefore, the greatest possible number of groups is 25.
40. To find the greatest possible dimensions of each square, we need to find the largest square that can evenly divide both the length (35m) and the width (15m) of the community garden.
First, let's find the factors of 35: 1, 5, 7, and 35.
Next, let's find the factors of 15: 1, 3, 5, and 15.
Looking at the lists of factors, we see that the largest common factor of 35 and 15 is 5.
Therefore, the greatest possible dimensions of each square in the community garden would be 5m by 5m.
Let me know if there's anything else I can assist you with!
No problem! I'll break down each problem and explain how to find the answer.
39. To find the greatest possible number of groups, we need to find the common factor between 50 and 75. In this case, the common factor is 25. So, if we form groups of 25 boys and 25 girls, we can have the maximum number of groups. To get the number of groups, we divide the total number of boys or girls by the common factor. In this case, the greatest possible number of groups is 50 boys / 25 = 2 groups.
40. To find the greatest possible dimensions of each square, we need to find the greatest common divisor (GCD) of the length and width of the community garden. In this case, the GCD of 35 and 15 is 5. So, we can divide the garden into squares with sides of 5 meters. To find the number of square gardens, we divide the length of the garden by the side length of each square. In this case, the greatest possible number of square gardens is 35 meters / 5 meters = 7 square gardens.
Now, let's move on to the next problems. Feel free to ask for help with any specific question you have!