1. **State the problem:** We need to find the cost of one iPhone given the total costs of purchases made by James and Peter. 2. **Define variables:** Let $x$ be the cost of one iPhone and $y$ be the cost of one Android phone. 3. **Write the system of equations based on the problem:** - James bought 3 iPhones and 4 Android phones for 6350 cedis: $$3x + 4y = 6350$$ - Peter bought 4 iPhones and 3 Android phones for 6950 cedis: $$4x + 3y = 6950$$ 4. **Solve the system of equations:** Multiply the first equation by 3 and the second by 4 to eliminate $y$: $$9x + 12y = 19050$$ $$16x + 12y = 27800$$ 5. **Subtract the first new equation from the second:** $$16x + 12y - (9x + 12y) = 27800 - 19050$$ $$7x = 8750$$ 6. **Solve for $x$:** $$x = \frac{8750}{7} = 1250$$ 7. **Interpretation:** The cost of one iPhone is 1250 cedis. **Final answer:** $$\boxed{1250}$$