To determine who saves the most of their salary each month among Josh, Amira, and Lucas, let's analyze their savings patterns step-by-step.
### Josh's Savings
Josh saves 18% of his salary each month.
If Josh's monthly salary is [tex]\( S \)[/tex], then his monthly savings amount is:
[tex]\[ \text{Josh's Savings} = \frac{18}{100} \times S = 0.18S \][/tex]
In percentage terms, this is:
[tex]\[ \text{Josh's Savings Percentage} = 18\% \][/tex]
### Amira's Savings
Amira spends [tex]\(\frac{4}{5}\)[/tex] of her salary each month. This means she saves the remaining portion of her salary.
If Amira's monthly salary is [tex]\( S \)[/tex], then her spending amount is:
[tex]\[ \text{Amira's Spending} = \frac{4}{5} \times S = 0.8S \][/tex]
Thus, the amount she saves is:
[tex]\[ \text{Amira's Savings} = S - 0.8S = 0.2S \][/tex]
In percentage terms, this is:
[tex]\[ \text{Amira's Savings Percentage} = 20\% \][/tex]
### Lucas's Savings
For Lucas, the ratio of the amount he saves to the amount he spends is 3:1.
This ratio implies that for every 4 parts of his salary, he saves 3 parts and spends 1 part.
If we consider Lucas’s monthly salary [tex]\( S \)[/tex], let's divide it into 4 parts:
[tex]\[ \text{Total parts} = 3 \text{ (savings)} + 1 \text{ (spending)} = 4 \][/tex]
Lucas's savings portion is:
[tex]\[ \text{Lucas's Savings} = \frac{3 \text{ parts}}{4 \text{ parts}} \times S = \frac{3}{4} \times S = 0.75S \][/tex]
In percentage terms, this is:
[tex]\[ \text{Lucas's Savings Percentage} = 75\% \][/tex]
### Comparing Savings Percentages
Now that we have calculated the savings percentages for each individual, we can compare them:
- Josh saves 18% of his salary.
- Amira saves 20% of her salary.
- Lucas saves 75% of his salary.
Among the three, Lucas saves the highest percentage of his salary each month, which is 75%.
### Conclusion
Hence, Lucas saves the most of his salary each month.
[tex]\[ \boxed{\text{Lucas}} \][/tex]
