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To determine which prescription drug coverage option is the least expensive for Emmeline, we need to consider both the monthly premium and the prescription co-pay for each option. Emmeline's family averages two prescriptions per month.
Here's the detailed step-by-step calculation for each option:
### Option A:
- Monthly Premium: \[tex]$50 - Prescription Co-pay: \$[/tex]20 per prescription
The total monthly cost for Option A can be calculated as:
[tex]\[ \text{Total Cost for Option A} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$50 + (\$20 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$50 + \$40 \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$90 \][/tex]
### Option B:
- Monthly Premium: \[tex]$70 - Prescription Co-pay: \$[/tex]15 per prescription
The total monthly cost for Option B can be calculated as:
[tex]\[ \text{Total Cost for Option B} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$70 + (\$15 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$70 + \$30 \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$100 \][/tex]
### Option C:
- Monthly Premium: \[tex]$90 - Prescription Co-pay: \$[/tex]10 per prescription
The total monthly cost for Option C can be calculated as:
[tex]\[ \text{Total Cost for Option C} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$90 + (\$10 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$90 + \$20 \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$110 \][/tex]
### Option D:
- Monthly Premium: \[tex]$110 - Prescription Co-pay: \$[/tex]0 per prescription
The total monthly cost for Option D can be calculated as:
[tex]\[ \text{Total Cost for Option D} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
Since the prescription co-pay is \[tex]$0: \[ \text{Total Cost for Option D} = \$[/tex]110 + (\[tex]$0 \times 2) \] \[ \text{Total Cost for Option D} = \$[/tex]110 \]
Now, we summarize the total monthly costs for each option:
- Option A: \[tex]$90 - Option B: \$[/tex]100
- Option C: \[tex]$110 - Option D: \$[/tex]110
Comparing these costs, we see that Option A, with a total monthly cost of \$90, is the least expensive option.
Therefore, Emmeline's least expensive option is Option A.
Here's the detailed step-by-step calculation for each option:
### Option A:
- Monthly Premium: \[tex]$50 - Prescription Co-pay: \$[/tex]20 per prescription
The total monthly cost for Option A can be calculated as:
[tex]\[ \text{Total Cost for Option A} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$50 + (\$20 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$50 + \$40 \][/tex]
[tex]\[ \text{Total Cost for Option A} = \$90 \][/tex]
### Option B:
- Monthly Premium: \[tex]$70 - Prescription Co-pay: \$[/tex]15 per prescription
The total monthly cost for Option B can be calculated as:
[tex]\[ \text{Total Cost for Option B} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$70 + (\$15 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$70 + \$30 \][/tex]
[tex]\[ \text{Total Cost for Option B} = \$100 \][/tex]
### Option C:
- Monthly Premium: \[tex]$90 - Prescription Co-pay: \$[/tex]10 per prescription
The total monthly cost for Option C can be calculated as:
[tex]\[ \text{Total Cost for Option C} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$90 + (\$10 \times 2) \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$90 + \$20 \][/tex]
[tex]\[ \text{Total Cost for Option C} = \$110 \][/tex]
### Option D:
- Monthly Premium: \[tex]$110 - Prescription Co-pay: \$[/tex]0 per prescription
The total monthly cost for Option D can be calculated as:
[tex]\[ \text{Total Cost for Option D} = \text{Monthly Premium} + (\text{Prescription Co-pay} \times \text{Number of Prescriptions}) \][/tex]
Since the prescription co-pay is \[tex]$0: \[ \text{Total Cost for Option D} = \$[/tex]110 + (\[tex]$0 \times 2) \] \[ \text{Total Cost for Option D} = \$[/tex]110 \]
Now, we summarize the total monthly costs for each option:
- Option A: \[tex]$90 - Option B: \$[/tex]100
- Option C: \[tex]$110 - Option D: \$[/tex]110
Comparing these costs, we see that Option A, with a total monthly cost of \$90, is the least expensive option.
Therefore, Emmeline's least expensive option is Option A.
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