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.