Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

The correct option is 7.

Let's break down the relationship between the number of machines, the time taken, and the number of toys produced step-by-step:

First, we are given that 7 machines take 7 minutes to make 7 identical toys.
This means that all 7 machines are working simultaneously for the entire duration of 7 minutes. Together, they produce 7 toys.
From this, we can determine the rate of a single machine. If 7 machines working together for 7 minutes produce 7 toys, it implies that each individual machine takes exactly 7 minutes to produce 1 toy.

Now, we want to find out how many minutes it would take for 100 machines to make 100 toys at the same rate.
Since the machines operate independently and concurrently, we can have 100 machines working at the same time.
If each machine takes 7 minutes to make 1 toy, then 100 machines working simultaneously for 7 minutes will produce:
$100\times 1=100$ toys.

Therefore, it will take exactly 7 minutes for 100 machines to make 100 toys.