Which of the following sets is closed under division?
2 answers:
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Answer:
a) Smallest line that can be made with each color = 300 cm
b) Total strips should be used = 47 strips
c) Total strips used of blue color = 20
Total strips used of green color = 15
Total strips used of red color = 12
Step-by-step explanation:
Given - To decorate a wall, there are 15 cm blue, 20 cm green, and 25 cm red strips of paper. On the wall you want to build three lines of the same size, one of each color and without cutting any strip.
To find - a) How long is the smallest line that can be made with each color?
b) How many strips should be used?
c) How many of each color?
Proof -
a)
For the smallest line that can be made with each color, we just have to find the lcm (least common multiple) of the 3 srtips.
Firstly,
Decompose the 3 strips to its prime factors , we get
15 = 3×5
20 = 2²×5
25 = 5²
So,
The Lcm(15, 20, 25) = 3×2²×5² = 3×4×25 = 300
∴ we get
Smallest line that can be made with each color = 300 cm
b)
Now,
Total strips used = 300 cm
Strips used by 15 cm blue = = 20 strips
Strips used by 20 cm green = = 15 strips
Strips used by 25 cm red = = 12 strips
So,
Total strips should be used = 20 + 15 + 12 = 47 strips
c)
Total strips used of blue color = 20
Total strips used of green color = 15
Total strips used of red color = 12
