CEO Salaries In 2002, hourly wages for the top three

CEOs (chief executive officers) of U.S. corporations
were calculated based on their working 14 hours per
day for 365 days. Together the three CEOs made
$44,000 per hour. The top CEO earned $2,000 more per
hour than the combined hourly wages of the next two
top CEOs, and the top CEO earned $7,000 more per
hour than the next top CEO.

(a) Let x, y, and z be the hourly wages in thousands
of dollars for the top CEOs from greatest to least.
Write a system of equations whose solution gives
these hourly wages.

(b) Solve the system. Interpret the answer.

(c) The average American worker earned $16.23 per
hour in 2002. How many hours did the average
American work to earn an amount equal to one
hour of work by the top CEO in 2002?

(a) We can write the following system of equations:

x + y + z = 44000 (equation 1)
x = y + 2000 (equation 2)
x = z + 7000 (equation 3)

(b) To solve this system, we can substitute equations 2 and 3 into equation 1:

(y + 2000) + y + (y - 7000) = 44000

Simplifying this equation gives:

3y - 5000 = 44000

Now solving for y:

3y = 49000

y = 16333.33

Substituting the value of y back into equations 2 and 3 gives:

x = 16333.33 + 2000 = 18333.33
z = 16333.33 - 7000 = 9333.33

So the solution to the system of equations is x = 18333.33, y = 16333.33, and z = 9333.33.

Interpretation: The hourly wages for the top CEOs from greatest to least are $18,333.33, $16,333.33, and $9,333.33.

(c) To find out how many hours the average American worker had to work to earn an amount equal to one hour of work by the top CEO, we divide the CEO's hourly wage by the average American worker's hourly wage:

18333.33 / 16.23 = 1131.77

Therefore, the average American worker would need to work approximately 1132 hours to earn an amount equal to one hour of work by the top CEO.

(a) To write a system of equations based on the given information, let's first assign variables to the unknowns.

Let x, y, and z represent the hourly wages in thousands of dollars for the top CEOs from greatest to least.

From the given information, we can write the following equations:

1. Together, the three CEOs made $44,000 per hour:
x + y + z = 44

2. The top CEO earned $2,000 more per hour than the combined hourly wages of the next two CEOs:
x = y + z + 2

3. The top CEO earned $7,000 more per hour than the next top CEO:
x = y + 7

(b) To solve the system of equations, we will substitute the values given by equation 2 and 3 into equation 1:

Substituting equation 2 into equation 1:
(y + z + 2) + y + z = 44
2y + 2z + 2 = 44
2y + 2z = 42
Dividing both sides by 2:
y + z = 21

Substituting equation 3 into equation 1:
(y + 7) + y + z = 44
2y + z + 7 = 44
2y + z = 37

We now have a system of two equations with two variables:

y + z = 21 ...(4)
2y + z = 37 ...(5)

Subtracting equation 4 from equation 5:
(2y + z) - (y + z) = 37 - 21
y = 16

Substituting the value of y into equation 4:
16 + z = 21
z = 21 - 16
z = 5

Substituting the value of y and z into equation 1:
x + 16 + 5 = 44
x + 21 = 44
x = 44 - 21
x = 23

The solution to the system of equations is:
x = 23
y = 16
z = 5

Interpretation: The hourly wage of the top CEO is $23,000, the hourly wage of the second-highest CEO is $16,000, and the hourly wage of the third-highest CEO is $5,000.

(c) To find out how many hours the average American worker worked to earn an amount equal to one hour of work by the top CEO in 2002, we need to compare their wages.

The average American worker earned $16.23 per hour. To calculate the number of hours they need to work to earn an amount equal to one hour of work by the top CEO, we can divide the top CEO's hourly wage by the average American worker's wage:

$23,000 / $16.23 = 1,418.42

The average American worker would need to work approximately 1,418.42 hours to earn an amount equal to one hour of work by the top CEO in 2002.