A trader bought 2 cows and 9 goats for ksh. 98,200. If she had bought 3 cows and 4 goats, she would have spent ksh. 2,200 less. Form two equations and find the cost of a cow and a goat.

Let $c$ be the cost of one cow in Ksh.
Let $g$ be the cost of one goat in Ksh.

"A trader bought 2 cows and 9 goats for a total of ksh. 98,200."

"If she had bought 3 cows and 4 goats, she would have spent ksh. 2,200 less."
Ksh. 2,200 less than Ksh. 98,200 is $98200 - 2200 = 96000$.

The two equations are:

Let $A = \begin{bmatrix} 2 & 9 \\ 3 & 4 \end{bmatrix}$.

The cost of a cow is $\boxed{\text{Ksh } 24,800}$ and the cost of a goat is $\boxed{\text{Ksh } 5,400}$.

Profit on cow = 30%
Selling Price per cow ($SP_c$) = $24800 \times (1 + 0.30) = 24800 \times 1.30 = 32240$ Ksh.

Profit on goat = 40%
Selling Price per goat ($SP_g$) = $5400 \times (1 + 0.40) = 5400 \times 1.40 = 7560$ Ksh.

Total received = $(2 \times SP_c) + (9 \times SP_g)$
Total received = $(2 \times 32240) + (9 \times 7560)$
Total received = $64480 + 68040$
Total received = 132520 Ksh.
The total amount of money she received is $\boxed{\text{Ksh } 132,520}$.

Total cost = $2c + 9g = 2(24800) + 9(5400) = 49600 + 48600 = 98200$ Ksh.
(This matches the initial total cost given in the problem statement).

Total profit = Total received - Total cost
Total profit = $132520 - 98200 = 34320$ Ksh.

The first four significant figures are 3, 4, 9, 4. The fifth digit is 9, so we round up the fourth digit.
Percentage Profit $\approx 34.95\%$
The percentage profit is $\boxed{34.95\%}$.