Business Math and Algebra Research Paper

Managerial Math

Solve each of the following equations for the unknown variable.

a) 15x + 40 = 8x -

15x +49 = 8x

49= -7x

b) 7y - 1 = 23-5y

Y=

c) 9(2x + 8) = 20 - (x + 5)

= 15-x

d) 4(3y - 1) - 6 = 5(y + 2)

Y = (20/7)

Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the second, he lost 4%. His total profit was $9,600. How much did he pay for each piece of land?

X= price of the first plot

Y= price of the second plot

X+Y= 110,000

.16x-.04y=9600

x=110,000-y

.16(110,000-y)-.04y=9600

17600-.16y-.04y=9600

y=40,000

x=110,000-40,000=70,000

A major car rental firm charges $57 a day with unlimited mileage. A discount firm offers a similar car for $24 a day plus 22 cents per mile. How far must you drive in a day in order for the cost to be the same at both firms?

Answer:

57=24+.22X

.22X=57-24

.22X=

X=33/.22

X=150 MILES.

Algebraic Operations and Applications

When solving the following questions, show each step of the solution along with the final results. If there is no work to show, be sure to fully explain your solution method.

1. Simplify the following algebraic operations:

a) 7x -- 2(x-2) + 5(x+3)

7x-2x+4 + 5x +15

10x + 19

b) (x+2)(x-4) + 3x + 1

x^2 + x -7

2. Suppose a student has earned the following grades on her first four quizzes: 83, 72, 89, 78. What must she score on her fifth quiz in order to have a mean of 80 on all of her quizzes?

322 + x = 400

3. The perimeter of a rectangle is twice the length plus twice the width. The area of a rectangle is the product of its length and width. Suppose we let l represent the length and w represent the width of a rectangle.

a) Write an algebraic expression that represents the perimeter.

b) Write an algebraic expression that represents the area.

c) Calculate the perimeter of a rectangle 12 inches long and 20 inches wide.

d) Calculate the area of the rectangle described in Part C.

III. Managerial Math

7) Divide the following numbers:

a) +2/+2 = 2

b) +2/-2 = -2

c) -2/-2 = 2

8) Add the following numbers:

a) (-10) + (-20) = -30

b) (+10) + (-20) = -10

9) Subtract the following numbers:

a) (-20) -- (-30) = 10

b) (-20) -- (+30) = -50

c) (+20) -- (-30) = 50

10) Evaluate the following exponentials:

a) (-1)^3 = -1

b) -- 1^3 = -1

c) (-1)^2 = 1

d) -- 1^2 = -1

IV. Linear Equations and Applications

Linear Equations and Applications:

1. Find the x- and y-intercepts for the line given by the equation 3x + 2y = 12

X= 4 y=6

2. Find the equation of the line that passes through the points (3,1) and (2,-1). Write the equation in slope-intercept form.

Y = 2x-5

3. Find the equation of the line that passes through the points (1,1) and (-2,10). Write the equation in slope-intercept form.

Y = 4 -- 3x

4. Suppose a business purchases a new tractor at an original cost of $42,000. Further, suppose this tractor has a useful life of 8 years and a salvage value of $10,000.

a) Use the Straight-Line Method to find the yearly depreciation on this tractor.

(42000-10000) X 1/8 x 12/12 = 4000

b) How much is this tractor worth after 3 years?

V = -12000 + 42000 = 30,000

c) Find a formula that calculates the tractor's worth after t years. What is the maximum allowable value for t?

V = -4000(t) +…