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In every gram of gold, a goldsmith mixes \[0.25\] grams of silver and \[0.05\] grams of copper. What is the percentage of gold, silver and copper in every gram of gold?

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Last updated date: 23rd Jul 2024
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Answer
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Hint: Given problem can be solved by using the concept of percentage. and we can note that in the problem the composition of silver and copper is also given in terms of percentage so the whole quantity should be taken as 1 to calculate the percentage of gold in each gram.

Complete step-by-step answer:
Given: In every gram of gold, a goldsmith mixes \[0.25\] grams of silver and \[0.05\] grams of copper.
To find: the percentage of gold, silver and copper in every gram of gold
In 1 gram of gold there is \[0.25\] grams of silver and \[0.05\]grams of copper.
So, the amount of gold in the mixture is =total amount of mixture –(total gram of silver +total gram of copper)
In the problem total amount of mixture is not given so we have to assume it as 1
\[G = 1 - (0.25 + 0.05)\]
\[G = 1 - 0.3\]
\[G = 0.7\]
So, the mixture contains \[0.7\] gram of gold, and \[0.25\] grams of silver and \[0.05\] grams of copper.
The amount of gold in percentage is
\[G\% = 0.7 \times 100 = 70\% \]
The amount of silver in percentage is
\[S\% = 0.25 \times 100 = 25\% \]
The amount of copper in percentage is
\[C\% = 0.05 \times 100 = 5\% \]
Therefore, the percentage of gold, silver and copper in every gram of gold is \[70\% \] , \[25\% \]and \[5\% \] respectively.

Note: In mathematics percentage is number or ratio expressed as a fraction of 100. And we can convert any decimal to fraction by multiplying it with 100.In the above problem we have converted decimals to fraction by multiplying it with 100. Ex: \[0.25 \times 100 = 25\% \]