In one orphanage, for 72-day meal, cabbage was stored for 168 people, and in another orphanage 144-day meal was stored for 84 people. In which orphanage did they store more cabbage and how many times more?

Let's analyze the given data carefully: **Orphanage 1:** - Meal duration: 72 days - Number of people served: 168 **Orphanage 2:** - Meal duration: 144 days - Number of people served: 84 --- **Step 1: Understand what is stored** Assuming the amount of cabbage stored is proportional to the total "meal-days" it can provide. **Meal-days** = (Number of people served) × (Number of days) --- **Step 2: Calculate total meal-days stored in each orphanage** - **Orphanage 1:** \[ \text{Meal-days}_1 = 168 \times 72 \] - **Orphanage 2:** \[ \text{Meal-days}_2 = 84 \times 144 \] --- **Step 3: Compute the values** - \(\text{Meal-days}_1 = 168 \times 72\) Calculate: \[ 168 \times 72 = (160 + 8) \times 72 = 160 \times 72 + 8 \times 72 \] - \(160 \times 72 = 160 \times (70 + 2) = 160 \times 70 + 160 \times 2 = 11,200 + 320 = 11,520\) - \(8 \times 72 = 576\) Adding: \[ 11,520 + 576 = 12,096 \] So, **Meal-days for Orphanage 1: 12,096** - \(\text{Meal-days}_2 = 84 \times 144\) Calculate: \[ 84 \times 144 = (80 + 4) \times 144 = 80 \times 144 + 4 \times 144 \] - \(80 \times 144 = 80 \times (140 + 4) = 80 \times 140 + 80 \times 4 = 11,200 + 320 = 11,520\) - \(4 \times 144 = 576\) Adding: \[ 11,520 + 576 = 12,096 \] --- **Step 4: Compare** Both orphanages have stored an amount of cabbage capable of providing **12,096 meal-days**. **Answer:** They stored **the same amount of cabbage**. Therefore, neither has more than the other, and the ratio is 1:1. --- ## **Final answer:** **They stored the same amount of cabbage, so the ratio is 1:1.**