Step-by-step explanation:
To solve this problem, we need to find out how much iron should be added to the alloy to increase the percentage of iron to 90%.
Given:
- Initial weight of the alloy = 50g
- Initial percentage of iron in the alloy = 80%
- Final percentage of iron required = 90%
Let's calculate the amount of iron in the initial alloy:
Amount of iron in the initial alloy = 80% of 50g = 0.8 * 50g = 40g
Let x be the amount of iron added to the alloy to achieve a 90% iron content.
The total weight of the alloy after adding iron will be 50g (initial alloy weight) + x (iron added).
Now, the new percentage of iron in the alloy will be:
(40g + x) / (50g + x) = 90%
Solving this equation:
(40 + x) / (50 + x) = 0.90
40 + x = 0.90 * (50 + x)
40 + x = 45 + 0.90x
0.10x = 5
x = 50g
Therefore, the amount of iron that should be added to the alloy to increase the percentage of iron to 90% is 50g, which is option (A).
