I have deduced and found three equations in which I need to solve this problem (Stated Below) How can I format this to fit into matrices to be solved with Cramers rule.
The formulas I have are:
R=100000
C = 0.1(R-(P+F))
P = 0.05(R-(C))
F = 0.4(R-(C=F))
Would the matrix look similar to
0.1 1 1
0.5 1 0
0.4 1 1
Is this correct and if not where did I go wrong :/, thank you! <3
Full Question: A company earns before-tax profits of 100,000 dollars. It has agreed to contribute 10 percent of its after-tax profits to the Red Cross Relief Fund. It must pay a provincial tax of 5 percent of its profits (after the Red Cross donation) and a federal tax of 40 percent of its profit (after the donation and provincial taxes are paid). Use Cramer’s rule to determine how much the company pays in provincial taxes, federal taxes, and Red Cross donation. {Hint: Let C, P, and F represent the amounts of the charitable donation, provincial tax, and federal tax, respectively. Since after-tax profits are $100,000 – (P+F), therefore: C = 0.1 [100,000 – (P+F) ]. Use the other pieces of information given in this question to write two other equations, one for P and one for F. Solve these equations simultaneously using Cramer’s rule.}
Steps
Original Matrix
P C F
Determinate = -0.957
0.1____1_____0.1 = 10000
1_____0.05____0 = 5000
0.4___0.4_____1 = 40000
P C F
Determinate = -4500
10000____1_____0.1 = 10000
5000_____0.05____0 = 5000
40000___0.4_____1 = 40000
P C F
Determinate = -5700
0.1____10000_____0.1 = 10000
1_____5000____0 = 5000
0.4___40000_____1 = 40000
P C F
Determinate = -37620
0.1____1_____10000 = 10000
1_____0.05____5000 = 5000
0.4___0.4_____40000 = 40000
Then I just divided P, C, F determinate by the original one
You need to do a little algebra to put the equations into the format $xP + yC + zF = w$ where $x,y,z,w$ are constants.
R=100000
$C = 0.1(R-(P+F))$ => $C = 10000 - 0.1(P+F)$ => $0.1P + C + 0.1F = 10000 $
$P = 0.05(R-(C))$ => $P = 5000 - 0.05C$ => $P + 0.05C + 0F = 5000$
$F = 0.4(R-(C=F))$ => becomes something, depending on what your typo here means.
Can you take it from here?