i could use some major guidance for this problem. I got number 1a with Y = federal taxes, and Z = state taxes.
any help is greatly greatly appreciated
----------------------------------------------------------------------------------
A company gives bonuses based on the amount of profit it makes each year. It must balance morale (through higher bonuses) against the amount of profit they want to keep. The following project asks you to explore what happens to the profits as bonuses are increased, and to make a recommendation.
Consolidated Business Merchandizing (CBM) made a $800,000 profit this year before paying bonuses and state and federal taxes.
1. Suppose CBM decides to pay employees a bonus that is 2% of the profit, after state and federal taxes are deducted. Then state taxes of 6% are paid on the profit after bonuses are paid. Federal taxes are 34% of the profit that remains after bonuses and state taxes are deducted.
a.) Identify the three unknowns, above.
x = total employee bonus
y =
z =
b.) Algebraically translate the sentence, “The bonus is 2% of the profit of $800,000 after state and federal taxes are deducted.”
To translate, think of a word-for-word translation:
The bonus write the variable for the bonus
is write the symbol that stands for “is”
2% of write in decimal form
the profit of $800,000 translate the word deducted and use
after state and federal taxes are deducted the correct variables
Use parenthesis so as to take 2% of all of this last part.
Finally, put this all together in one algebraic statement.
c.) Translate the sentence, “The state taxes are 6% of the profit of $800,000 after bonuses are paid.”
d.) Translate the sentence, “Federal taxes are 34% of the profit of $800,000 after bonuses and state taxes are deducted.”
2. a.) Simplify each equation and rewrite in the form ax+by+cz = constant. Show your work.
b.) Write the three equations in the form of an augmented matrix.
c.) Enter the matrix into your calculator and solve using rref. Write the solution matrix.
d.) Identify the solution:
x = y = z =
e.) Write a sentence explaining the solution.