Questions: Sylvanite is a mineral that contains 28.0% gold by mass. How much sylvanite would you need to dig up to obtain 64.0 g of gold? Express your answer with the appropriate units.

Sylvanite is a mineral that contains 28.0% gold by mass. How much sylvanite would you need to dig up to obtain 64.0 g of gold? Express your answer with the appropriate units.
Transcript text: Sylvanite is a mineral that contains $28.0 \%$ gold by mass. How much sylvanite would you need to dig up to obtain 64.0 g of gold? Express your answer with the appropriate units.
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to find out how much sylvanite is required to obtain 64.0 g of gold, given that sylvanite is 28.0% gold by mass.

Step 2: Set Up the Equation

Let \( x \) be the mass of sylvanite needed. Since 28.0% of the mass of sylvanite is gold, we can write the equation: \[ 0.28x = 64.0 \, \text{g} \]

Step 3: Solve for \( x \)

To find \( x \), divide both sides of the equation by 0.28: \[ x = \frac{64.0}{0.28} \]

Step 4: Calculate the Mass of Sylvanite

Perform the division to find \( x \): \[ x = 228.5714 \, \text{g} \]

Step 5: Round to Appropriate Significant Figures

Round the result to four significant figures: \[ x = 228.6 \, \text{g} \]

Final Answer

The mass of sylvanite needed is \(\boxed{228.6 \, \text{g}}\).

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