Question

How many grams of active ingredient do you need to fortify 200g of 5% cream to 10%?

Answer 1

To determine how many grams of active ingredient you need to fortify 200g of 5% cream to 10%, you can follow these steps:

1. **Find the amount of active ingredient in the 5% cream.**
\[
\text{Amount of active ingredient} = \text{cream weight} \times \text{percentage} = 200g \times 0.05 = 10g
\]

2. **Determine the total amount of active ingredient needed for the 10% cream.**
\[
\text{Total weight of cream} = 200g + x
\]
where \(x\) is the amount of active ingredient to be added.

The total amount of active ingredient needed for 10% cream is:
\[
\text{Amount of active ingredient needed} = 10\% \text{ of total cream weight} = 0.10 \times (200g + x)
\]

3. **Set up the equation.**
The current amount of active ingredient plus the amount added must equal the amount needed for 10% cream:
\[
10g + x = 0.10 \times (200g + x)
\]

4. **Expand and rearrange the equation.**
\[
10g + x = 20g + 0.10x
\]
\[
10g + x - 0.10x = 20g
\]
\[
10g + 0.90x = 20g
\]
\[
0.90x = 20g - 10g
\]
\[
0.90x = 10g
\]

5. **Solve for \(x\).**
\[
x = \frac{10g}{0.90}
\]
\[
x \approx 11.11g
\]

You need approximately **11.11 grams** of the active ingredient to fortify the 200g of 5% cream to 10%.