Linda West, a dental lab technician, pays three times as much

Mathematics

1 answer:

Natalka [10]3 years ago

6 0

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

_____

<em>Additional comment</em>

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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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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Solution to the problem

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