Subjects algebra

Charity Contributions 332756

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem statement:** Given a charity association contributed $\frac{5}{12}$ of the total amount, the municipality contributed $\frac{2}{4}$, and the rest was contributed by a group of benefactors. The total amount is 300000. 2. **Show that the municipality contributed a larger share than the charity association:** We compare the fractions $\frac{5}{12}$ and $\frac{2}{4}$. Convert $\frac{2}{4}$ to $\frac{6}{12}$ to have a common denominator. Since $\frac{6}{12} > \frac{5}{12}$, the municipality contributed more. 3. **Express the fraction contributed by the benefactors:** Total contribution fractions sum to 1: $$\text{Benefactors' share} = 1 - \left(\frac{5}{12} + \frac{2}{4}\right) = 1 - \left(\frac{5}{12} + \frac{6}{12}\right) = 1 - \frac{11}{12} = \frac{1}{12}$$ 4. **Calculate the amount contributed by the benefactors and the charity association together:** Sum of their shares: $$\frac{5}{12} + \frac{1}{12} = \frac{6}{12} = \frac{1}{2}$$ Amount contributed: $$300000 \times \frac{1}{2} = 150000$$ **Final answer:** The benefactors and the charity association together contributed 150000.