The problem provides a table showing the current month's incoming amount, consumption amount, and inventory amount for various prefectures. It also includes the change from the previous month for each of these quantities. The problem asks how many months it will take for the inventory amounts of Miyagi and Okinawa to be reversed, assuming the inventory changes by the same amount each month. The unit is in thousands of cubic meters. The formula for calculating current month's inventory is given as: Current month's inventory = Previous month's inventory + Current month's incoming amount - Current month's consumption amount.

1. Problem Description

The problem provides a table showing the current month's incoming amount, consumption amount, and inventory amount for various prefectures. It also includes the change from the previous month for each of these quantities. The problem asks how many months it will take for the inventory amounts of Miyagi and Okinawa to be reversed, assuming the inventory changes by the same amount each month. The unit is in thousands of cubic meters. The formula for calculating current month's inventory is given as:

Current month's inventory = Previous month's inventory + Current month's incoming amount - Current month's consumption amount.

2. Solution Steps

First, we extract the relevant data from the table for Miyagi and Okinawa:

Miyagi:

Current Inventory: 207

Change from previous month: +3

Okinawa:

Current Inventory: 255

Change from previous month: -6

Let $M_n$ be the inventory of Miyagi after $n$ months and $O_n$ be the inventory of Okinawa after $n$ months.

We can express the inventory after $n$ months as:

$M_n = 207 + 3n$

$O_n = 255 - 6n$

We want to find the smallest integer $n$ such that $M_n > O_n$.

$207 + 3n > 255 - 6n$

$9n > 48$

$n > \frac{48}{9} = \frac{16}{3} = 5.333...$

Since $n$ must be an integer, the smallest integer value of $n$ that satisfies this inequality is $n = 6$.

So, after 6 months, Miyagi's inventory will be greater than Okinawa's inventory.

Let's calculate the inventory after 6 months:

$M_6 = 207 + 3*6 = 207 + 18 = 225$

$O_6 = 255 - 6*6 = 255 - 36 = 219$

Therefore, after 6 months, the inventory of Miyagi (225) will be greater than the inventory of Okinawa (219).

3. Final Answer

6 months