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Citrus2011 [14]
3 years ago
9

A magic carpet is made with three different colors of yarn. The ratio of each color is shown below. 10 parts gold yarn, 7 parts

bronze yarn, and 3 parts silver yarn. The magic carpet is made with total of 150 meters of yarn. How much silver is in the carpet?
Mathematics
1 answer:
serious [3.7K]3 years ago
7 0

Answer: 22.5 yards

Step-by-step explanation:

There are a total of 20 parts yarn. This means that 3/20 of the carpet is silver. So in order to compare this to the 150 meters of total yarn, you would set up this equation:

3/20 = x/150

Next, you cross multiply:

3*150 = 20*x or simplified would be 450 = 20x

Next, you divide both sides by 20 to get x by itself.

450/20 = 22.5, so x is equal to 22.5

This means you have 22.5 yards of silver in the carpet.

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Answer:

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Now,

Sum =  \frac{a( {r}^{n} - 1) }{(r - 1)}   \\

So,

\frac{a( {r}^{n} - 1)}{(r - 1)}  = 728 \\  \frac{2( {3}^{n} - 1) }{(3 - 1)}  = 728 \\  \frac{2( {3}^{n} - 1) }{2}  = 728 \\  {3}^{n}  - 1 = 728 \\ {3}^{n}=728+1\\ {3}^{n}  = 729 \\  {3}^{n}  =  {3}^{6}  \\ \boxed{ n = 6}

Therefore, number of terms is 6

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Answer:

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