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…

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.