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.

To understand why this is correct, let's break down the rate of production step-by-step.

First, we are given that 7 machines take 7 minutes to make 7 identical toys.
Since all 7 machines work simultaneously, we can determine the time it takes for a single machine to make a single toy. If 7 machines working together for 7 minutes produce 7 toys, it means that each individual machine is working independently to produce exactly 1 toy in those same 7 minutes.

Therefore, the rate of 1 machine is:
1 machine = 1 toy in 7 minutes.

Now, we want to find how many minutes it would take for 100 machines to make 100 toys at the same rate.
Since each of the 100 machines works independently and simultaneously at the same rate, each machine will be responsible for making exactly 1 toy.
As established, it takes 1 machine exactly 7 minutes to make 1 toy. Thus, if 100 machines start working at the same time, each making 1 toy, they will finish making 100 toys in exactly 7 minutes.