Step 1: Determine the fraction of rice remaining after Day 1. The school used $\frac{1}{6}$ of the total rice on the first day. Fraction remaining after Day 1 is: $$1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{5}{6}$$ Step 2: Determine the fraction of rice used on Day 2. On the second day, $\frac{1}{5}$ of the remaining rice was used. Fraction used on Day 2 = $\frac{1}{5} \times (\text{fraction remaining after Day 1})$ $$\frac{1}{5} \times \frac{5}{6} = \frac{1}{6}$$ Step 3: Determine the total fraction of rice used on Day 1 and Day 2. Total fraction used = (Fraction used on Day 1) + (Fraction used on Day 2) $$\frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$$ a) Step 4: Determine the fraction of rice that was shared equally for the last 4 days. The "rest of the rice" was shared equally for the last 4 days. This is the fraction remaining after Day 2. Fraction remaining after Day 2 = $1 - (\text{Total fraction used after Day 2})$ $$1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$$ This is the fraction of rice shared equally for the last 4 days. The fraction of rice that was shared equally for the last 4 days is $\boxed{\frac{2}{3}}$. b) Step 5: Determine the fraction of the total rice used on the last day. The fraction $\frac{2}{3}$ of the total rice was shared equally over 4 days (Day 3, Day 4, Day 5, Day 6). The amount used on each of these 4 days is $\frac{1}{4}$ of this remaining fraction. Fraction used on the last day (Day 6) = $\frac{1}{4} \times \frac{2}{3}$ $$\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}$$ Step 6: Calculate the total mass of rice the school had bought. We know that the mass used on the last day was 37.5 kg, which corresponds to $\frac{1}{6}$ of the total mass. Let $T$ be the total mass of rice bought. $$\frac{1}{6} T = 37.5 \text{ kg}$$ To find $T$, multiply both sides by 6: $$T = 37.5 \times 6$$ $$T = 225 \text{ kg}$$ The mass of rice that the school had bought is $\boxed{225 \text{ kg}}$. Send me the next one 📸