1. **State the problem:** A company gave a total of 15500 to three charities: Charity A received 4000, Charity B received 5500, and Charity C received the remaining amount. We need to find the ratio of the amounts received by Charity A, Charity B, and Charity C in simplest form. 2. **Find the amount Charity C received:** $$\text{Amount for Charity C} = 15500 - (4000 + 5500)$$ $$= 15500 - 9500 = 6000$$ 3. **Write the ratio of amounts received:** $$4000 : 5500 : 6000$$ 4. **Simplify the ratio:** Find the greatest common divisor (GCD) of 4000, 5500, and 6000. - Prime factors: - 4000 = $2^5 \times 5^3$ - 5500 = $2^2 \times 5^3 \times 11$ - 6000 = $2^4 \times 3 \times 5^3$ The common factors are $2^2$ and $5^3$, so GCD = $4 \times 125 = 500$. 5. **Divide each term by 500:** $$\frac{4000}{500} : \frac{5500}{500} : \frac{6000}{500} = 8 : 11 : 12$$ 6. **Final answer:** The simplest form of the ratio is $$\boxed{8 : 11 : 12}$$