To solve this problem, we need to determine if any child has a ratio of chocolates to total candies that equals [tex]\(\frac{1}{4}\)[/tex].
Let's break it down step by step for each child:
### Juan:
1. Total Candies: 54
2. Chocolates: 12
We calculate the ratio of chocolates to total candies:
[tex]\[
\text{Juan's ratio} = \frac{\text{Chocolates}}{\text{Total Candies}} = \frac{12}{54}
\][/tex]
### Lorena:
1. Total Candies: 60
2. Chocolates: 15
We calculate the ratio of chocolates to total candies:
[tex]\[
\text{Lorena's ratio} = \frac{\text{Chocolates}}{\text{Total Candies}} = \frac{15}{60}
\][/tex]
### Luis:
1. Total Candies: 40
2. Chocolates: 10
We calculate the ratio of chocolates to total candies:
[tex]\[
\text{Luis's ratio} = \frac{\text{Chocolates}}{\text{Total Candies}} = \frac{10}{40}
\][/tex]
Next, we need to compare these ratios with the target ratio, which is [tex]\(\frac{1}{4}\)[/tex].
We can see the numerical results:
- Juan's ratio: [tex]\(0.2222...\)[/tex] which is approximately [tex]\(\frac{2}{9}\)[/tex]
- Lorena's ratio: [tex]\(0.25\)[/tex] which is exactly [tex]\(\frac{1}{4}\)[/tex]
- Luis's ratio: [tex]\(0.25\)[/tex] which is exactly [tex]\(\frac{1}{4}\)[/tex]
### Conclusion:
From the calculations:
- Juan does not have a ratio of [tex]\(\frac{1}{4}\)[/tex].
- Lorena has a ratio of [tex]\(\frac{1}{4}\)[/tex].
- Luis has a ratio of [tex]\(\frac{1}{4}\)[/tex].
Therefore, the children who have a quantity of chocolates equal to [tex]\(\frac{1}{4}\)[/tex] of their candies are Lorena and Luis.
