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Linda West, a dental lab technician, pays three times as much
for dental insurance as she does for vision insurance and three times as
much for health insurance as for vision and dental combined. Linda's
employer pays 40% of the cost for all three. If the total annual premium
for all three is $9,360, how much will Linda pay biweekly for (a) vision,
(b) dental, and (c) health insurance?

Sagot :

sqdancefan

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

_____

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.

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