Determine the quantity of the dealer that paid for the car and the profit the dealer made.

Bei iliyoandikwa (Marked Price) ni Ksh. 450,000.
Punguzo ni $7\%$.
Kiasi cha punguzo ni:

$$\text{Kiasi cha punguzo} = \frac{7}{100} \times 450,000 = 31,500 \text{ Ksh.}$$

Bei ya kuuza (SP) ni:

$$\text{SP} = 450,000 - 31,500 = 418,500 \text{ Ksh.}$$

Muuzaji alipata faida ya $13\%$ juu ya bei ya kununua (CP). Hii inamaanisha kuwa bei ya kuuza (SP) ni $100\% + 13\% = 113\%$ ya bei ya kununua.
Hivyo,

$$\text{SP} = 1.13 \times \text{CP}$$

Tunajua SP = Ksh. 418,500, kwa hiyo:

$$418,500 = 1.13 \times \text{CP}$$

Ili kupata CP, gawanya SP kwa 1.13:

$$\text{CP} = \frac{418,500}{1.13}$$ $$\text{CP} \approx 370,353.9823$$

Kiasi cha pesa muuzaji alicholipa kwa gari, tukizungusha hadi senti mbili, ni:

$$\text{CP} = \boxed{\text{Ksh. } 370,353.98}$$