Calculate the Price of a 100g Alloy: Iron-Aluminum Cost Breakdown

To solve this problem, we'll follow these steps:

• Identify the contribution of the aluminum component to the overall cost.

• Identify the contribution of the iron component to the overall cost.

• Combine the contributions to find the total cost of the alloy.

Let's perform the calculations:

1. Aluminum's Contribution:
The alloy is 30% aluminum, which costs 5 per 100 grams. Hence, the contribution from aluminum is:
\( 0.30 \times 5 = 1.5 \text{ dollars}

2. Iron's Contribution:
The alloy is 70% iron, which costs 17 per 100 grams. Hence, the contribution from iron is:
\( 0.70 \times 17 = 11.9 \text{ dollars}

3. Total Cost of the Alloy:
To obtain the total cost of 100 grams of the alloy, we add the contributions from both components:
$1.5 + 11.9 = 13.4 \text{ dollars}$

Therefore, the price of 100 grams of the alloy is $13.4 \text{ dollars}$.