Cengage Financial Algebra 1st Edition Chapter 1 Exercise 1.1 The Stock Market

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Financial Algebra 1st Edition Chapter 1 The Stock Market

Page 6 Problem 1 Answer

Given: Jillian owns60%of the stock in a private catering corporationThere are1,200shares in the entire corporation

To find: The number of shares owned by Jillian

Solution: We will assume that the number of shares owned by Jillian is x

Write the data given as a fraction and solve for x

Let’s assume that the number of shares owned by Jillian is x

60/100=x/1200

[writing the data given as proportion]

72000=100x

[cross multiply]

720=x

[divide both sides by100]

If Jillian owns60% of the stock in a private catering corporation and there are1,200 shares in the entire corporation then he owns 720 shares

Cengage Financial Algebra 1st Edition Chapter 1 Exercise 1.1 The Stock Market

Page 6 Problem 2 Answer

Given: Two partners are starting a wedding planning business. The total investment is$45,000 in the ratio of 4:5

To find: The contribution of each investor

Solution: We will convert the ratio in the form of x Write an equation for investment by each investor and solve it

The investment is in the ratio of 4:5

So, the investment will be 4x and 5x

The equation showing the investment will be:

4x+5x=45,000

9x=45,000

[combine like terms]

x=5000

[divide each side by 9]

Thus investments will be:

4x=4(5000)=20,000

5x=5(5000)

=25,000

The total investment in the wedding planning business by two investors is of $45,000 in the ratio of4:5

Thus, the investment by the investors is of $20,000 and $25,000 respectively.

Page 7 Problem 3 Answer

The quote by Thomas Edison “Genius is 1% inspiration and 99%  perspiration.

Accordingly, a genius is often merely a talented person who has done all of his or her homework” talks about the importance of hard work.

Here the scientist has emphasized that only having a bright idea and inspiration is not enough to get success, it is more essential to put in the efforts and do hardwork to get success.

In the given quote of Thomas Edison, the words ‘Genius is1% inspiration and99%  perspiration’ shows the importance of efforts in achieving success.

Here, the word perspiration is used to show hardwork.In this lesson, we have learned how investment is made in an organization.

Just like the quote says, only having an idea of good business won’t give results, it requires investments and efforts to get results.

Page 7 Problem 4 Answer

Given: Ryan owns three-eighths of a florist shop worth$76,000

To find: The value of Ryan’s share of the business

Solution: Multiply the ownership proportion with the value of the business.

Ryan’s share of business= Ownership proportion× Total value of business

=3/8×76,000

=28,500

Ryan owns three-eighths of a florist shop worth $76,000, which means his share is of$28,500

Page 7 Problem 5 Answer

Given: A corporation issues1,200,000 shares of stock at its beginning to shareholders.

To find: Number of shares a shareholder must own to have a majority of the shares

Solution: To hold the majority of shares, a shareholder must hold at least one share more than 50% shares.

We will multiply the total number of shares by 50% and add 1

To hold the majority share, a shareholder must own at least the following number of shares:

=[50%×total number of shares]+1

=[50%×1,200,000]+1

=600,001

A corporation issues1,200,000 shares of stock at its beginning to shareholders then a shareholder must own atleast 600,001 shares to have a majority of the shares.

Page 7 Problem 6 Answer

Given: A corporation issues1,200,000 shares of stock at its beginning to shareholders.

To find: Number of shares a shareholder must own to have a majority of the shares

Solution: To hold the majority of shares, a shareholder must hold at least one share more than50% shares.

We will multiply the total number of shares by 50% and add 1

To hold the majority share, a shareholder must own at least the following number of shares:

=[50%×total number of shares]+1

=[50%×1,200,000]+1

A corporation issues1,200,000 shares of stock at its beginning to shareholders then a shareholder must own atleast600,001 shares to have a majority of the shares.

Page 7 Problem 7 Answer

Given: Julie and Kristen are the partners in a local sporting goods shop They needed $51,000  to start the business so they invested in the ratio 5:12 , respectively.

To find: Money invested by each partner

Solution: Write the ratio in the form of x

Write an equation showing the ownership and solve for x

The investment will be 5x and12x

We will now write the equation for ownership:

5x+12x=51,000

17x=51,000

[combine like terms]

x=3000

[divide each side by 17]

Investments by each partner are:

Investment by Julie=5x=5(3000)

=15,000

Investment by Kristen=12x

=12(3000)

=36,000

Julie and Kristen invest in the ratio of 5:12 for the total investment of $51,000

This means, Julie invests$15,000 and Kristen invests$36,000

Page 7 Problem 8 Answer

Given: Julie and Kristen are the partners in a local sporting goods shop They needed $51,000  to start the business so they invested in the ratio 5:12, respectively.

Thus, Julie invests$15,000 and Kristen invests $36,000

To find: The percent of the business owned by Kristen

Solution: Write Kristen’s investment as a proportion of total investment Multiply the proportion by100 to get the percentage.

We can also first divide the proportion, get the answer in decimals and then multiply by 100 to get the percentage.

Proportion of ownership by Kristen=Kristen′s investment

Total investment    =36,000/51,000

=36/51

=12/17

Percentage ownership=12/17×100

=70.5882%

≈70.6%

[rounded off to the nearest tenth of a percentage]

Julie and Kristen invest in the ratio of 5:12 for the total investment of $51,000

So, Kristen owns 70.6% of the business.

Page 7 Problem 9 Answer

Given: Julie and Kristen are the partners in a local sporting goods shop and invest in the ratio of 5:12 Investment by Kristen is70.6%

To find: The percent of business that Julie will own if the business grows to $3,000,000

Solution: The amount of total investment does not change the proportion of investment by each partner as the ratio of investment remains the same at 5:12

So, increase in the amount to $3,000,000 from $51,000 has no change in ownership percentage

Percentage of Julie’s ownership=100%−ownership of Kristen

=100%−70.6%

=29.4%

Julie and Kristen invest in the ratio of 5:12 for the total investment of $51,000

Even if the amount increases to$3,000,000 the ratio remains the same as before and so Julie will own29.4%

Page 7 Problem 10 Answer

Given: Joe, Thea, and Taylor invested in a partnership in the ratio1:4:7, respectively.

When the partnership was worth $1.6 million, Thea decides to go to graduate school and sells her part of the partnership to Joe

To find: The amount Joe need to pay Thea to buy her share of the business

Solution: Convert the ratio into an algebraic equation and solve for x Using that find the value of investment of Thea.

Let x represent the amount invested by Joe, 4x represent the amount invested by Thea and7x represent the amount invested by Taylor.

We will use the ratio to write an algebraic equation and solve it for x:

1x+4x+7x=16,00,000

12x=16,00,000

x=16,00,000/12

x=4,00,000/3

x=133,333.33

Value of Thea’s share=4x=4(133,333.33)

=533333.333

≈533,333

[rounded off to nearest dollar]

 

Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7, respectively.

Joe needs to pay Thea$533,333 to buy her share of the business when the value of the business is$1.6 million.

Page 7 Problem 11 Answer

Given: Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7 , respectively.

Thea sold her share to Joe when the total value of the investment was$1.6 million

To find: Percent of the business owned by Joe after he buys Thea’s portion

Solution: We will first write the new ownership ratio.Find the value of Joe’s share and then find its percentage

The new ownership ratio between Joe and Taylor will be 5:7

So, we can say Joe’s share is 5x and Taylor’s share is7x.

So, 5x+7x=1,600,000

12x=1600000

[combine like terms]

x=133333.33

[divide each side by12]

Thus Joe’s share will be

5x=5(133333.33)

=666666.67

Percentage of Joe’s ownership: =666666.67

1600000×100

=41.7%

[rounded off to nearest tenth of a percentage]

Joe, Thea, and Taylor invested in a partnership in the ratio1:4:7, respectively If Thea sells her share to Joe, then his new ownership percentage will be41.7%

Page 8 Exercise 1 Answer

Given: Seventy-two percent of the shareholders in a service corporation are women.

The corporation is owned by 45,600 people

To find: The number of shareholders that are women

Solution: Write the percentage as a fractionWrite a proportion for the situation given

Write the percentage as a fraction

72%=72/100

Let x represent women shareholders. So,

72/100=x/45600

[write a proportion]

3283200=100x

[cross multiply]

32832=x

If the corporation is owned by 45,600 people and seventy-two percent of the shareholders in a service corporation are women, then 32,832 shareholders are women.

Page 8 Exercise 2 Answer

The 120 shareholders of a corporation are voting for a new Board of Directors.

Shareholders receive one vote for each share they own.

So if the shareholder will own even one share more than50%  then it will mean that he owns majority of the shares and in that case it will be possible for one shareholder’s votes to choose the new Board of Directors.

The 120 shareholders of a corporation are voting for a new Board of Directors.

Shareholders receive one vote for each share they own.

Thus, it would be possible for one shareholder’s votes to choose the new Board of Directors only if that shareholder owns the majority of shares i.e. more than 50% of shares.

Page 8 Exercise 3 Answer

Given: The ownership of the corporation is represented by 2,351,000  shares of stock owned by 111,273  shareholders.

To find: Must all of the shareholders own more than one share of stock?

Solution: The shareholding pattern can be different for each shareholder.

For example, 111272 shareholders can hold 1 share each and the remaining one shareholder can hold all the remaining shares.

There can be many other combinations possible like the one mentioned above.

The ownership of the corporation is represented by 2,351,000  shares of stock owned by 111,273 shareholders.

In this case, it is not essential that all the shareholders should own more than one stock.

For instance, all111,272 can hold one share each and the remaining shareholder can hold the remaining majority of shares.

Page 8 Exercise 4 Answer

Given: The ownership of the corporation is represented by 2,351,000 shares of stock owned by111,273  shareholders.

To find: The percentage of shareholders represented in the meeting if 3,411  shareholders attend the meeting

Solution: We will first write the shareholders attending as a proportion to the total shareholdersThen find its percentage

Let x be the percentage of shareholders present 3411/111273=x/100

341100=111273x

[cross multiply]

3.065=x

[divide each side by111273]

x≈3%

[rounding off to nearest percentage]

If 3411 shareholders attend the meeting from 111273 shareholders, then 3% of shareholders are represented in the meeting.

Page 8 Exercise 5 Answer

Given: The ownership of the corporation is represented by 2,351,000 shares of stock owned by111,273 shareholders.

To find: The percent of the shares that are represented at the meeting if the shareholders who do attend own a combined 1.8 million shares

Solution: We will write the situation as a proportion

Let x be the percentage of shares represented by the shareholders attending the meeting

1,800,000/2,351,000=x/100

180,000,000=2,351,000x

[ cross multiply]

76.56=x

[divide each side by2351000]

x≈77%

[rounded off to nearest percentage]

When the shareholders who attend the meeting own a combined 1.8 million shares of the corporation out of the total 2,351,000  shares,  it represents 77%  of the shares at the meeting.

Page 7 Exercise 6 Answer 

The top x shareholders in a corporation each own y shares of a certain stock The corporation’s ownership is represented by a total of w shares of stock

To find: The percent of the corporation owned by the top x shareholders

Solution: Find the total number of shares owned by the top x shareholders Find the percentage of that holding

The number of shares held by the top x shareholders= number of top shareholders× shares held by each of those shareholders

=x×y

=xy

Proportion held by the top x shareholders=xy/w

Percentage holding=xy/w×100

=100xy/w%

Where the top x shareholders in a corporation each own y shares of a certain stock and the corporation’s ownership is represented by a total of w  shares of stock then the percent of the corporation owned by the top x shareholders is100 xy/w%

Page 8 Exercise 7 Answer

Given: A sole proprietorship is worth w dollars. The owner loses a lawsuit against him for y dollars where y  is greater than w.

To find: Express algebraically the value of the personal property the owner must forfeit to pay the settlement.

Solution: In a sole proprietorship, the owner is personally liable for losses over and above the value of the business.

So, Value of personal property to be forfeited(P)=Loss−value of business

=y−w

A sole proprietorship is worth w dollars.

The owner loses a lawsuit against him for y  dollars where y  is greater than w

The value of the personal property(P) the owner must forfeit to pay the settlement can be expressed algebraically as: P=y−w

Page 8 Exercise 8 Answer

Given: Six equal partners own a local pizzeria and bought many personal items such as cars, boats, new homes, and so on from the profit.

In order to protect their personal possessions, they decide to incorporate the pizzeria, so that the six partners own shares in the corporation and have limited liability.

The business is worth $675,000.

To find: After an accident, the partners lose a lawsuit and have to pay $1.2 million in damages.

We have to find how much money will each partner personally lose to pay this lawsuit

Solution: In the case of a partnership, the partners are personally liable for losses greater than the capital of the business.

But, in a corporation, the shareholders have limited liability, as in they are only responsible for the amount of each share and nothing more.

Their personal property is not forfeited in case of loss.

Here, the partners converted the pizzeria to a corporation and became shareholders and will have limited liability.

So the loss exceeding the business worth cannot be recovered from those partners.

Six equal partners own a local pizzeria. As the partners made a tremendous profit they bought many personal items such as cars, boats, new homes, and so on.

In order to protect their personal possessions, they decide to incorporate the pizzeria, so that the six partners own shares in the corporation and have limited liability.

The business is worth$675,000.

After an accident, the partners lose a lawsuit and have to pay$1.2 million in damages.

But as the partners are now shareholders, they have limited liability and so they will personally lose othing to pay this lawsuit

Page 8 Exercise 9 Answer

Given: Three people invest in a business. The first two invest in the ratio 2:3, and the third person invests twice as much as the other two combined.

The total investment is$30 million.

To find: The value of the investment by the major investor

Solution: We will convert the ratio into an algebraic equation showing total investment and solve it.

Let the three partners be A,B,C

So, investment by A will be 2x and investment by B will be3x

Thus, Investment by C=2(2x+3x)

=2(5x)

=10x

Total investment=A+B+C

30=2x+3x+10x

[substitute values]

30=15x

[combine like terms]

2=x

[divide each side by15]

Investment byC=10x

=10(2)

=20 million dollars

Three people invest in a business The first two invest in the ratio 2:3, and the third person invests twice as much as the other two combined.

The total investment is $30 million.So, the major investor contributed $20 million.

Page 8 Exercise 10 Answer

Given: Three people invest in a business. The first two invest in the ratio 2:3, and the third person invests twice as much as the other two combined.

The total investment is $30 million.The major investor has invested$20 million.

To find: If the major investor own more than half the business

Solution: We will find the value of half the business Check if the value of the investment by the major investor is greater than that amount Value of half of the business=30/2

=15 million dollars

The investment by the majority holder is $30 million.

So , we can say that the major investor own more than half the business

Three people invest in a business. The first two invest in the ratio2:3, and the third person invests twice as much as the other two combined.

The total invested is $30 million and from the data we can find that the major investor has invested$20 million Thus, the major investor own more than half the business.

Page 8 Exercise 11 Answer

The major investor has invested $20 million The total investment is$30 million

To find: The fraction of the business the major investor owns

Solution: The fraction of investment by major investor=investment by major investor total investment

=20/30

=2/3

Three people invest in a business. The first two invest in the ratio2:3, and the third person invests twice as much as the other two combined.

The total investment is$30 million and from this data we can find that the major investor has invested $20 million Thus, the major investor owns 2/3 rd  of the business

Page 8 Exercise 12 Answer

Given: Ten years ago, Lisa bought a hair salon for x dollars.

She built up the business and it is now worth nine times what she paid for it

To find: The amount Lisa’s friend must pay Lisa to buy half the business.

Solution: Find the current value of the business Divide that by 2  to find the value of half of the business

Original value of hair saloon=x

dollarsCurrent value of hair saloon=9x

dollarsValue of half the business=9x/2

=4.5x dollars

Ten years ago, Lisa bought a hair salon for x dollars and its current value is 9x dollars.

So, the amount Lisa’s friend must pay Lisa to buy half the business is 4.5x dollars

Page 8 Exercise 13 Answer

Four people invested in a restaurant. One person invested$100,000.

Two others invested in the ratio x:2x, and the fourth person invested an amount equal to the other three investors combined.

So, the expression for the investment by fourth person(D) will be: D=100000+3x

Page 8 Exercise 14 Answer

Given: Four people invested in a restaurant. Let the investors be A,B,C,D

Their investments are:

A=$100,000

B=x

C=2x

D=A+B+C   =100000+3x

The total investment was $1,100,000

To find: Equation that allows you to find the amount invested by each person

Solution: Total investment(T)=A+B+C+D

1100000=100000+x+2x+(100000+3x)

[substitute values]

1100000=200000+6x

[Combine like terms]

Four people invested in a restaurant. One person invested$100,000.

Two others invested in the ratiox:2x, and the fourth person invested an amount equal to the other three investors combined.

The equation that allows you to find the amount invested by each person is:

1100000=200000+6x

Page 8 Exercise 15 Answer

Given: Four people invested in a restaurant. Let the investors be A,B,C,D

Their investments are:

A=$100,000

B=x

C=2x

D=A+B+C=100000+3x

The total investment(T)  was $1,100,000

To find: Investment by each person

Solution: We will write the given data as an expression for total investment and solve for x

Total Investment=A+B+C+D

1100000=100000+x+2x+(100000+3x)

1100000=200000+6x

900000=6x

150000=x

So value of investment:

A=$100000

B=x   =$150000

C=2x  =2(150000)

=$300000

D=100000+3x

=100000+3(150000)

=100000+450000

=$550000

Four people invested in a restaurant. One person invested $100,000.

Two others invested in the ratiox:2x, and the fourth person invested an amount equal to the other three investors combined.

So, if the investors areA,B,C,Dthen the investments are:

A=$100,000

B=$150,000

C=$300,000

D=$550,000

Chapter 1 Solving Linear Equations

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