Certainly! Let's dive into the problem step by step to find the sugar concentration in the two solutions, A and B.
### Given Data:
- Solution A:
- Sugar: 30 grams
- Water: 250 grams
- Solution B:
- Sugar: 5 grams
- Water: 250 grams
### Objective:
We want to determine the concentration of sugar in each solution. Concentration in this context is defined as the amount of sugar per gram of water.
### Step-by-Step Solution:
#### Solution A:
1. Calculate the concentration of sugar in solution A:
- Sugar: 30 grams
- Water: 250 grams
The concentration of sugar in solution A can be found by dividing the amount of sugar by the amount of water.
[tex]\[
\text{Concentration}_A = \frac{\text{Sugar in grams}}{\text{Water in grams}} = \frac{30 \text{ g}}{250 \text{ g}}
\][/tex]
2. Perform the division:
[tex]\[
\text{Concentration}_A = 0.12 \text{ g of sugar per g of water}
\][/tex]
#### Solution B:
1. Calculate the concentration of sugar in solution B:
- Sugar: 5 grams
- Water: 250 grams
Similarly, the concentration of sugar in solution B is given by:
[tex]\[
\text{Concentration}_B = \frac{\text{Sugar in grams}}{\text{Water in grams}} = \frac{5 \text{ g}}{250 \text{ g}}
\][/tex]
2. Perform the division:
[tex]\[
\text{Concentration}_B = 0.02 \text{ g of sugar per g of water}
\][/tex]
### Conclusion:
- The concentration of sugar in Solution A is [tex]\( \mathbf{0.12} \)[/tex] grams of sugar per gram of water.
- The concentration of sugar in Solution B is [tex]\( \mathbf{0.02} \)[/tex] grams of sugar per gram of water.
These final values represent the sugar concentration in each solution.
