Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

  $machines6:10time(in min)1:4 ⋮⋮ 270:x$ 

=> 6 * 1 * x = 10 * 4 * 270

=> x= 1800