Question

A magic carpet is made with three colors of yarn. The ratio of each color in the carpet is shown below: 101010 parts gold yarn 777 parts bronze yarn 333 parts silver yarn PART A The magic carpet is made with a total of 150150150 meters of yarn.

Answer 1

Given:

A magic carpet is made with three different colours of yarn

The ratio of each colour is:- 10 parts of gold yarn, 7 parts bronze yarn, and 3 parts silver yarn.

The magic carpet is made with a total of 150 meters of yarn.

To find:

How much each of the 3 colours is in the carpet?

Solution:

The total meters of the yarn in the magic carpet = 150

The ratio of gold, bronze and silver yarn is = 10 : 7 : 3

Let's assume,

"10x" → represents the meters of gold colour

"7x" → represents the meters of bronze colour

"3x" → represents the meters of silver colour

Now, we can write the equation as:

$10x + 7x + 3x = 150$

$\implies 20x = 150$

$\implies x = \frac{150}{20}$

$\implies x = 7.5$

Therefore,

Gold colour → 10x = 10 × 7.5 = 75

Bronze colour → 7x = 7 × 7.5 = 52.5

Silver colour → 3x = 3 × 7.5 = 22.5

Thus, the meters of each colour present in the yarn of the magic carpet:

$\boxed{\bold{Gold \rightarrow \underline{75\:m}}}\\\\\boxed{\bold{Bronze \rightarrow \underline{52.5\:m}}}\\\\\boxed{\bold{Silver \rightarrow \underline{22.5\:m}}}$

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