Calculate the Price of Hydrogen in a Gas Mixture

A mixture contains 3 gases:

Helium constitutes 3% of the mixture and costs $7 per 100 grams.<br><br>Hydrogen constitutes 87$11 per 100 grams.

If the mixture sells for $X per 100 grams, then what is the price of hydrogen?

To solve this problem, we'll apply a weighted average approach to determine the cost of hydrogen in the mixture:

• Step 1: Calculate the contribution of helium per 100 grams. $\text{Cost of helium per 100 grams} = 3\% \times 7 = 0.21$ dollars.
• Step 2: Calculate the contribution of oxygen per 100 grams. $\text{Cost of oxygen per 100 grams} = 10\% \times 11 = 1.1$ dollars.
• Step 3: Write the equation for the total cost per 100 grams. $X = 0.21 + \text{Cost of hydrogen per 100 grams} + 1.1$
• Step 4: Simplify the equation to solve for the cost of hydrogen per 100 grams. $\text{Cost of hydrogen per 100 grams} = X - (0.21 + 1.1)$ $\text{Cost of hydrogen per 100 grams} = X - 1.31$
• Step 5: Express the cost of hydrogen based on its percentage in the mixture. Since hydrogen makes up 87%, $\frac{87}{100} \times \text{Cost of hydrogen per 100 grams} = X - 1.31$
• Step 6: Solve for the cost of hydrogen. $\text{Cost of hydrogen} = \frac{100}{87} \times (X - 1.31) \approx 1.15X - 1.51$

Therefore, the price of hydrogen is $1.15X - 1.51$ dollars per 100 grams.