4. Oketch sells his car to Jane and makes a profit of $$ 17 \% $$. Jane sells the same car to Issa at $$ \mathrm{Sh} .300,000 $$, making a loss of $$ 10 \% $$. Determine the price at which Oketch bought the car. $$ \quad $$ ( 3 marks)

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To determine the price at which Oketch bought the car, we can follow these steps:

1. **Let $$ P $$ be the price at which Oketch bought the car.**
2. **Since Oketch sells the car to Jane at a profit of $$ 17\% $$, the selling price (SP) for Oketch can be calculated as:**
   $$
   SP = P + 0.17P = 1.17P
   $$

3. **Jane sells the car to Issa for $$ \text{Sh} 300,000 $$ at a loss of $$ 10\% $$. This means Jane's selling price is $$ 90\% $$ of her buying price (which is the same as Oketch's selling price). Therefore, we can express Jane's selling price as:**
   $$
   300,000 = 0.90 \times SP
   $$

4. **Substituting the expression for $$ SP $$ from step 2 into the equation:**
   $$
   300,000 = 0.90 \times 1.17P
   $$

5. **Now, we can solve for $$ P $$:**
   $$
   300,000 = 1.053P
   $$
   $$
   P = \frac{300,000}{1.053}
   $$
   $$
   P \approx 284,000.38
   $$

Thus, the price at which Oketch bought the car is approximately **Sh 284,000.38**.
The price at which Oketch bought the car is approximately Sh 284,000.38.

4. Oketch sells his car to Jane and makes a profit of \( 17 \% \). Jane sells the same car to Issa at \( \mathrm{Sh} .300,000 \), making a loss of \( 10 \% \). Determine the price at which Oketch bought the car. \( \quad \) ( 3 marks)

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