A factory making tomato soup has 400 kg of tomatoes delivered each week. The factory uses a percentage of the tomatoes each week to make the soup. After how many weeks does the factory need to take delivery of any more tomatoes because it still has enough from the previous week?

- 72% used = 288 kg
- 28% remaining = 112 kg

- Week 1: 112 kg remaining
- Week 2: 224 kg remaining
- Week 3: 336 kg remaining

Each week, the factory receives [tex]$400$[/tex] kg of tomatoes. Out of these, [tex]$72\%$[/tex] are used for the soup, which amounts to

[tex]$$0.72 \times 400 = 288 \text{ kg.}$$[/tex]

This means that the remaining tomatoes left at the end of the week equal

[tex]$$400 - 288 = 112 \text{ kg.}$$[/tex]

The leftover tomatoes accumulate week by week. We need to find after how many weeks the accumulated leftover is at least [tex]$400$[/tex] kg so that the delivery is no longer necessary.

Let the number of weeks be [tex]$n$[/tex]. Since each week leaves [tex]$112$[/tex] kg unused, the total leftover after [tex]$n$[/tex] weeks is

[tex]$$112 \times n.$$[/tex]

We set up the inequality to determine [tex]$n$[/tex]:

[tex]$$112 \times n \ge 400.$$[/tex]

Dividing both sides by [tex]$112$[/tex] we get:

[tex]$$n \ge \frac{400}{112} \approx 3.57.$$[/tex]

Since [tex]$n$[/tex] must be a whole number (you can’t have a fraction of a week in this context), we round up to the next whole number. Thus, [tex]$n = 4$[/tex].

To confirm, let’s look at the cumulative totals:
- After Week 1: [tex]$112$[/tex] kg
- After Week 2: [tex]$112 \times 2 = 224$[/tex] kg
- After Week 3: [tex]$112 \times 3 = 336$[/tex] kg
- After Week 4: [tex]$112 \times 4 = 448$[/tex] kg

At Week 4, the cumulative leftover is [tex]$448$[/tex] kg, which is enough to meet the [tex]$400$[/tex] kg threshold.

Therefore, the factory does not need to take delivery of any more tomatoes after [tex]$\boxed{4}$[/tex] weeks.