Question

Emily has 32 grams of 25% sugar syrup, but this is just too sweet for her! How much water should she add to have 10% syrup?

Answer 1

To solve this problem, we can start by determining how much sugar is in the 32 grams of 25% sugar syrup.

1. **Calculate the amount of sugar in the syrup:**
\[
\text{Amount of sugar} = 25\% \text{ of } 32 \text{ grams} = 0.25 \times 32 = 8 \text{ grams}
\]

2. **Let \( x \) be the amount of water (in grams) that Emily needs to add to the syrup. After adding water, the total mass of the solution becomes \( 32 + x \) grams. We want the final concentration of sugar to be 10%. This is expressed as:
\[
\text{Concentration of sugar} = \frac{\text{Amount of sugar}}{\text{Total mass of solution}} = \frac{8}{32 + x}
\]
We want this to equal 10%, or 0.10:
\[
\frac{8}{32 + x} = 0.10
\]

3. **Solve for \( x \):**
- Multiply both sides by \( 32 + x \):
\[
8 = 0.10(32 + x)
\]
- Expand the right-hand side:
\[
8 = 3.2 + 0.10x
\]
- Rearranging gives:
\[
8 - 3.2 = 0.10x
\]
\[
4.8 = 0.10x
\]
- Divide by 0.10:
\[
x = \frac{4.8}{0.10} = 48
\]

Thus, Emily should add **48 grams of water** to obtain a 10% sugar syrup.