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Answer :
To determine the most economical way to purchase health insurance for the family, we need to compare the total costs for each option:
### Option 1: Insure the entire family through Patrick's employer
- Patrick's premium: Patrick's employer pays 100% of his premium, so Patrick's cost is [tex]$0.
- Additional beneficiaries: Susie and the twins (three additional beneficiaries) each have a premium of $[/tex]280 that Patrick’s employer will not cover.
So, the total cost for Patrick's employer is:
- For the additional beneficiaries: [tex]\( 3 \times \$280 = \$840 \)[/tex]
The total cost when insuring the whole family through Patrick's employer is \[tex]$840.
### Option 2: Insure the entire family through Susie's employer
- Susie's premium: Susie's employer pays 63% of her \$[/tex]403 premium. We calculate Susie's cost as the remaining 37%:
[tex]\( \$403 \times (1 - 0.63) = \$403 \times 0.37 = \$149.11 \)[/tex]
- Additional beneficiaries: Susie's employer offers to pay 63% of the \[tex]$310 premium for each additional beneficiary (Patrick and the twins), so Susie would pay 37% of the \$[/tex]310 for each:
[tex]\( 3 \times \$310 \times (1 - 0.63) = 3 \times \$310 \times 0.37 = \$344.10 \)[/tex]
The total cost when insuring the whole family through Susie’s employer is:
- For Susie and additional beneficiaries: [tex]\( \$149.11 + \$344.10 = \$493.21 \)[/tex]
### Conclusion
The most economical option is to insure the family through Susie's employer, with a total cost of \[tex]$493.21, as this option costs less compared to insuring through Patrick's employer, which totals \$[/tex]840.
### Option 1: Insure the entire family through Patrick's employer
- Patrick's premium: Patrick's employer pays 100% of his premium, so Patrick's cost is [tex]$0.
- Additional beneficiaries: Susie and the twins (three additional beneficiaries) each have a premium of $[/tex]280 that Patrick’s employer will not cover.
So, the total cost for Patrick's employer is:
- For the additional beneficiaries: [tex]\( 3 \times \$280 = \$840 \)[/tex]
The total cost when insuring the whole family through Patrick's employer is \[tex]$840.
### Option 2: Insure the entire family through Susie's employer
- Susie's premium: Susie's employer pays 63% of her \$[/tex]403 premium. We calculate Susie's cost as the remaining 37%:
[tex]\( \$403 \times (1 - 0.63) = \$403 \times 0.37 = \$149.11 \)[/tex]
- Additional beneficiaries: Susie's employer offers to pay 63% of the \[tex]$310 premium for each additional beneficiary (Patrick and the twins), so Susie would pay 37% of the \$[/tex]310 for each:
[tex]\( 3 \times \$310 \times (1 - 0.63) = 3 \times \$310 \times 0.37 = \$344.10 \)[/tex]
The total cost when insuring the whole family through Susie’s employer is:
- For Susie and additional beneficiaries: [tex]\( \$149.11 + \$344.10 = \$493.21 \)[/tex]
### Conclusion
The most economical option is to insure the family through Susie's employer, with a total cost of \[tex]$493.21, as this option costs less compared to insuring through Patrick's employer, which totals \$[/tex]840.
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