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amm1812
3 years ago
9

String A is 35 cm long. String B is five times as long as String A. Both are necessary to create a decorative bottle. Find the t

otal length of string needed for 17 identical decorative bottles. Express your answer in meters
Mathematics
1 answer:
Mamont248 [21]3 years ago
5 0

Length of string A = 35 cm

Length of string B = 5 times as long as String A

= 5\times35 = 175 cm

Assuming that whole length of string A and B is used to decorate one bottle

So if ,35 cm of string A and 175 cm of string B is needed for 1 bottle.

Hence, for 17 bottles string A needed is = 35\times17=595 cm

For 17 bottles string B needed is = 17\times175=2975 cm

In meters the length becomes;

1 cm = 0.01 meter

String A = 595 cm = 5.95 meter

String B = 2975 cm = 29.75 meter

And if these are added they become = 5.95+29.75 =35.70 meter

So, total length needed is = 35.70 meter ( if string A and B are added together)

Otherwise total String A needed is 5.95 meters and string B needed is 29.75 meters.


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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

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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,

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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 = \frac{300}{15} = 20 strips

Strips used by 20 cm green = \frac{300}{20} = 15 strips

Strips used by 25 cm red = \frac{300}{25} = 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

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