## Financial Algebra 1st Edition Chapter 5 Automobile Ownership

**Page 239 Problem 1 Answer**

Given: Annual premium is x dollars and surcharge on each semiannual payment is y dollars.

To find: The amount of his semiannual payment algebraically.

For doing so, we will refer to the fact that the amount of his semiannual payment is the sum of the annual premium and surcharge.

Dividing the annual premium by 2:x/2.

Adding the y-dollar surcharge:x/2+y.

Each of the two semiannual payments is x/2+y.

Each of the two semiannual payments is x/2+y.

**Page 240 Problem 2 Answer**

Given:Cost of fixing pole, bicycle, the car is x, y, w dollars respectively.

To find: The amount that can be claimed under Keith’s property damage liability insurance.

Total damage can be claimed.

Sum of the damages is x+y+w.

The amount that can be claimed under Keith’s property damage liability insurance is x+y+w.

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**Page 240 Problem 3 Answer**

Given: x dollars is deductible on comprehensive insurance. y dollars is the amount of damage.

To find: The cost that the insurance company pays.

The deductible amount is deducted from the total damage. So, the company pays y−x.

The company pays y−x.

**Page 241 Problem 4 Answer**

Given:50/100 BI liability insurance and$10,000 PIP insurance.

Owner hurts28 children each of whom needs$10,000 medical care.

To find: The amount the insurance company pays in total for these medical claims.

The owner has a maximum limit of$50,000 per person and a total limit of $100,000.

The owner needs28×$10,000=$280,000 for total medical expenses which is greater than the total limit of the insurance.

So, the company pays$100,000 and the rest is to be paid by the owner.

The amount the insurance company pays in total for these medical claims is$100,000.

**Page 242 Problem 5 Answer**

Given: We have learned the topics.To find: The quote in the context of what you learned.

The use of a car frequently leads to problems between parents and their children, which is why you should not lend your automobile to them.

Furthermore, adolescent drivers have the greatest accident rate, thus your children are more likely to be involved in an accident than other (older) persons.

The use of a car frequently causes friction between parents and their children, which is why you should never give your automobile to them.

**Page 242 Problem 6 Answer**

Given: Rachel has$25,000 worth of property damage insurance.

She causes$32,000 worth of damage to a sports car in an accident.

To find The damages that the insurance company have to pay.

When the amount of damage exceeds the insurance company’s coverage, the insurance company will pay the maximum amount of coverage.

So, the company pays$25,000.

The company pays$25,000.

**Page 242 Problem 7 Answer**

Given: The insurance company pays the maximum coverage of$25,000.

To find: The amount Rachel has to pay.

Here, the amount of damage exceeds the amount covered by the insurance company.

So, the owner pays the remaining claims of$32,000−$25,000=$7,000.

Rachel pays$7,000.

**Page 242 Problem 8 Answer**

Given: Ronald Kivetsky bought a new car and received these price quotes from his insurance company.

To find The annual premium.

The annual premium is the total of the insurance company’s quotes.

The annual premium is the total of the insurance company’s quotes.

So, the annual premium is $234+$266+$190+$11+$344+$410+$12=$1467.

The annual premium is$1467.

**Page 242 Problem 9 Answer**

Given: Annual premium is$1467.

To find: The semiannual premium.

For doing so, we will use the formula semiannual premium= annual premium/2.

We know that semiannual premium= annual premium/2

⇒$1,467÷2=$733.50.

The semiannual premium is$733.50.

**Page 242 Problem 10 Answer**

Given: Semiannual premium is$733.50.

To find: How much less would Ronald’s semiannual payments be if he dropped the optional collision insurance.

The owner pays the rest of the amount after the company pays.

The annual premium without collision insurance is $234+$266+$190+$11+$344+$12=$1057.

We know that semiannual premium = annual premium /2

$1,057÷2=$528.50.

The difference is$733.50−$528.50=$205

Ronald pays$205 less.

**Page 242 Problem 11 Answer**

Given : The annual premium is $924

We have to find the amounts of the three payments.

We will use some simple rule of percentage.

Here,The first payment is 40% of the annual premium.

So, 40%×$924=0.40×$924

=$369.60

The second and third payment is 30% of the annual premium.

So, 30%×$924=0.30×$924

=$277.20

Therefore,The three payments are: $369.60,$277.20,$277.20

**Page 242 Problem 12 Answer**

Given : Each person can collect up to$50,000

We have to find how much money must the insurance company pay out for these three people.

We will find it.

Here, The cost of a person that is beneath $50,000 are completely covered, that over $73,000

are covered up to $50,000.

So, $23,000+$500+$50,000=$73,500

Therefore,$73,500, the insurance company pay out for these three people.

**Page 242 Problem 13 Answer**

Given: Leslie submits a claim to her insurance company.

We have to find how much must Leslie pay for the repair.

We will find it.

Here, Leslie must pay the deductible which is $500

Therefore,$500 amount must Leslie pay for the repair.

**Page 243 Problem 14 Answer**

Given: Felix Madison has $10,000 worth of property damage insurance and a $1,000 deductible collision insurance policy.

He had a tire blowout while driving and crashed into a $1,400 fire hydrant.

The crash caused $1,600 in damages to his car.

We have to find which insurance covers the damage to the fire hydrant.

Here, The damage to the fire hydrant falls under the property damage insurance.

Therefore, Property damage insurance.

**Page 243 Problem 15 Answer**

Given:Felix Madison has $10,000 worth of property damage insurance and a $1,000 deductible collision insurance policy.

He had a tire blowout while driving and crashed into a $1,400 fire hydrant.

The crash caused $1,600 in damages to his car.

We have to find how much will the insurance company pay for the fire hydrant.

Here,As the damages to the fire hydrant is less than the total coverage, the insurance company pays the total damages.

So, $1,400

Therefore,$1,400amount will the insurance company pay for the fire hydrant.

**Page 243 Problem 16 Answer**

Given: Felix Madison has $10,000 worth of property damage insurance and a $1,000 deductible collision insurance policy.

He had a tire blowout while driving and crashed into a $1,400 fire hydrant.

The crash caused $1,600 in damages to his car.

We have to find which insurance covers the damage to the car.

Here,The damage to our own car is covered by the collision insurance policy.

Therefore,Collision insurance policy.

**Page 243 Problem 17 Answer**

Given : Felix Madison has$10,000 worth of property damage insurance and a$1,000 deductible collision insurance policy.

He had a tire blowout while driving and crashed into a $1,400

fire hydrant. The crash caused $1,600 in damages to his car.

We have to find how much will the insurance company pay for the damage to the car.

We will use above information.

Here, The insurance company pays the difference between the total damages to the car and the deductible.

So,$1,600−$1,000=$600

Therefore,$600 amount will the insurance company pay for the damage to the car

**Page 243 Problem 18 Answer**

Given: Eric must pay his p dollar annual insurance premium by himself.

We have to express how much he must save each month to pay this premium algebraically.

We will use above information.

Here,The amount he must save each month is the annual premium divided by the number of months in a year.

So, the amount is p/12

Therefore, he must save each month to pay this premium algebraically is p/12

**Page 243 Problem 19 Answer**

Given: Epic’s company raises his insurance 15% We have to express how much he must save each month to pay this premium algebraically.

We will use above information.

Here,The annual premium is increased by 15% of the premium i.e. p+15%×p=115%×p

Hence, the amount he must save each month is, 115%×p/12

Therefore, he must save each month to meet this new premium algebraically is115%×p/12

**Page 243 Problem 20 Answer**

Given: Mollie has 100/300/50 liability insurance and $50,000 PIP insurance.

We have to find what insurance will cover this, and how much will the company pay?.

We will use above information.

Here, In the given case, the pole and the minivan are public and private property, thus the damage will be covered by property damage.

Then is covered by the liability insurance.

Now,The total cost of the damage is the sum of the cost of the pole($7,000) and the cost of the damage to the minivan ($6,700).

i.e.Total cost

= Cost pole + Cost damage minivan

=$7,000+$6,700

=$13,700

So,The insured has a 100/300/50 liability insurance, where the last number 50

represents the insurance coverage of property damage and thus the insurance coverage is $50,000.

As the total cost of $13,700 is less than the insurance coverage of $50,000, the insurance company will pay the total cost of $13,700.

Therefore,Liability insurance (property damage) Company pays $13,700

**Page 243 Problem 21 Answer**

Given: The minivan’s driver sues for $4,000,000

We have to find what insurance will cover this, and how much will the company pay?.

We will use above information.

Here,As we know that the type of insurance that covers this is Bodily Injury insurance.

This type of insurance applies because the conditions are met: People are hurt and sues you for your negligence.

Now,The insurance company will pay the maximum of Kaylee’s insurance of$100,000

The first two numbers in 100/300/50 represent $100,000/$300,000 BI insurance.

The first number is the maximum amount the insurance company will pay to any one person.

Hence, the insurance company will pay the minivan’s driver $100,000

Therefore,Bodily Injury insurance,$100,000

**Page 243 Problem 22 Answer**

Given : The minivan’s driver (from part b) had medical bills totaling $60,000 from his hospital trip and physical therapy after the accident.

We have to find what insurance will cover this, and how much will the company pay.

We will use above information.

Here,As we know that the type of insurance that covers this is Personal Injury Protection insurance or PIP insurance.

This type of insurance applies because this insurance covers medical payments without regard to who is at fault.

Now,$50,000 PIP insurance means the insurance company will pay a limit of $50,000 per person, per accident.

Hence, The insurance company will pay the maximum amount of Kaylee’s insurance of $50,000

Therefore,

PIP insurance, $50,000

**Page 243 Problem 23 Answer**

Given : The three passengers in Mollie’s car are hurt and each requires $12,000 worth of medical attention.

We have to find what insurance will cover this, and how much will the company pay.

We will use above information.

Here, As we know that the type of insurance that covers this is Personal Injury Protection insurance or PIP insurance.

This type of insurance applies because this insurance covers medical payments without regard to who is at fault.

Now,$50,000 PIP insurance means the insurance company will pay a limit of $50,000 per person, per accident.

As there is no individual person who claims for more than $50,000

Hence, the insurance company will pay the entire amount of the medical expenses of $12,000×3=$36,000

Therefore,PIP insurance, $36,000

**Page 243 Exercise 1 Answer**

Given: The insurance company offers her a 35% discount for her annual premium.

We have to express algebraically the amount she must save each month to pay the new, lower premium.

We will use above information.

Here,The new premium is the previous premium decreased by 35% of the premium

i.e. x−35%×x=65%×x

Now,The amount she must save each month is then the new premium divided by the number of months in a year.

Hence,65%×x/12 Therefore, the amount she must save each month to pay the new, lower premium is 65%×x/12

**Page 244 Exercise 2 Answer**

Given: The annual premium would have been x dollars to insure the car, but they are entitled to a 10

percent discount since they have other cars with the company.

We have to express their annual premium after the discount algebraically.

We will use some simple percentage rule.

Here,The new premium is the previous premium decreased by 10% of the premium.

i.e. x−10%×x=90%×x

Therefore,90%×x,their annual premium after the discount is expressed algebraically.

**Page 244 Exercise 3 Answer**

Given: The Schuster family have to pay a y-dollar surcharge for this arrangement,

We have to express their quarterly payment algebraically.

We will use above information.

Here, We have, The annual premium is 90%×x

Now. the quarterly payment is :

90%×x/4+y

⇒22.5%×x+y

Therefore,The quarterly payment is,22.5%×x+y

**Page 244 Exercise 4 Answer**

Given: Marc currently pays x dollars per year for auto insurance

We have to express his annual premium for next year algebraically if he completes the course.

We will use above information.

Here,The new premium is the previous premium increased by 15% of the premium and decreased by the d dollars for completing the course.

So, x+15%×x−d=115%×x−d

Therefore,115%×x−d, his annual premium for next year is expressed algebraically

**Page 244 Exercise 5 Answer**

Given: The insurance company will lower his rate by d dollars.

We have to express his semiannual premium for next year algebraically if he does not complete the course.

We will use above information.

Here, The new premium is the previous premium increased by 15% of the premium.

i.e. x+15%×x=115%×x

Now, The semiannual premium is 115%×x/2

=57.5%×x

Therefore, The semiannual premium is 57.5%×x

**Page 244 Exercise 6 Answer**

Given: A stem-and-leaf plot which gives the number of juniors who took a driver education course at Guy Patterson High School over the last two decades.

We have to construct a box-and-whisker plot based on the data.

We will use above information.

Here,Firstly we have to order the data values from smallest to largest:41,42,43,45,45,46,51,51,58,58,58,59,60,60,60,61,62,65,71,71

So, the minimum (smallest data value) is 4.

Now, The median is the middle value of the sorted data set.

As there are 20 data values, the median is the average of the 10th and 11th data values : M=Q2

=58+58/2

=116/2

=58

The first quartile is the median of the data values below the median (or at 25% of the data).

As there are 10 data values below the median, the first quartile is the average of the 5th and 6th data value :Q1=45+46/2

=91/2

=45.5

The third quartile is the median of the data values above the median (or at 75%of the data).

As there are 10 data values above the median, the third quartile is the average of the 15th and 16th data value :Q3 =60+61/2

=121/2

=60.5

So, the maximum (largest data value) is 71

Now, The first quartile is at 25% of the sorted data list, the median at 50% and the third quartile at 75%.

So, the Box plot of the given data is,

Therefore,