Question

I mixed 84 grams of sugar with 156 grams of water. What percent of the syrup is sugar? What percent of the syrup is water?

Answer 1

To find the percentage of sugar and water in the syrup, we first need to determine the total mass of the syrup.

1. **Total mass of the syrup**:
\[
\text{Total mass} = \text{mass of sugar} + \text{mass of water} = 84 \, \text{grams} + 156 \, \text{grams} = 240 \, \text{grams}
\]

2. **Percentage of sugar in the syrup**:
\[
\text{Percentage of sugar} = \left( \frac{\text{mass of sugar}}{\text{total mass}} \right) \times 100 = \left( \frac{84}{240} \right) \times 100
\]
\[
\text{Percentage of sugar} = 0.35 \times 100 = 35\%
\]

3. **Percentage of water in the syrup**:
\[
\text{Percentage of water} = \left( \frac{\text{mass of water}}{\text{total mass}} \right) \times 100 = \left( \frac{156}{240} \right) \times 100
\]
\[
\text{Percentage of water} = 0.65 \times 100 = 65\%
\]

In conclusion, the syrup is:
- **35% sugar**
- **65% water**