Answer :
9514 1404 393
Answer:
- vision: $13.50
- dental: $40.50
- health: $162.00
Step-by-step explanation:
Let d, v, h represent the costs of dental, vision, and health insurance, respectively. The cost relations are ...
d = 3v . . . . . . . . . . . . . . . dental is 3 times vision
h = 3(v +d) . . . . . . . . . . . health is 3 times vision and dental combined
d + v + h = 9360 . . . . . annual premium
Substituting for h, we have ...
d + v + (3(d +v)) = 9360
Substituting for d, we have ...
3v +v +3(3v +v) = 9360
16v = 9360
v = 585
d = 3v = 1755
h = 3(d+v) = 7020
These are the total annual premiums. Linda pays 1/26 of 60% of this every two weeks. That fraction is 0.60/26 = 3/130.
a) Linda's biweekly vision insurance deduction is (585)(3/130) = $13.50
b) Linda's biweekly dental insurance deduction is (1755)(3/130) = $40.50
c) Linda's biweekly health insurance deduction is (7020)(3/130) = $162.00
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Additional comment
We know dental is 3v and health is 3(3v+v) = 12v = 4d. That is, once we find Linda's share of the biweekly vision premium, we can find the others by multiplying it by a suitable factor.
Final answer:
Linda's biweekly insurance payments are calculated based on her employer's 40% contribution and the total annual premium of $9,360. The calculated biweekly payments for vision, dental, and health insurance are approximately $13.50, $40.50, and $162.00, respectively.
Explanation:
Linda West needs to calculate her biweekly payment for vision, dental, and health insurance based on the total annual premium and her employer's contribution. Let's denote the cost of vision insurance as V, then the cost of dental insurance would be 3V and the cost for health insurance is 3(3V + V) = 12V, since it's three times the combined cost of vision and dental insurances. Given the total annual premium for all three insurances is $9,360 and her employer covers 40% of the cost, we can find the total cost Linda pays annually and then calculate her biweekly payment for each insurance.
To find the overall annual cost Linda pays:
Firstly, the total cost of all insurances together is 3V + 12V + V = 16V, which equals $9,360. Consequently, V equals $585 (which is obtained by dividing $9,360 by 16). This figure represents the annual cost of vision insurance before employer contribution. Knowing that Linda's employer pays 40% of the total costs, Linda is responsible for 60% of the amounts. Therefore, her annual payments for vision, dental, and health insurances would be 60% of their respective totals ($351 for vision, $1,053 for dental, and $4,212 for health insurance).
Then, to calculate the biweekly payment for each type of insurance, we divide the annual payment by 26 (the number of biweekly periods in a year):
- Vision: $351 / 26 = approximately $13.50
- Dental: $1,053 / 26 = approximately $40.50
- Health: $4,212 / 26 = approximately $162.00
This calculation shows how much Linda will pay every two weeks for each type of insurance.
