Running at the same constant rate, 6 identical machines can produce a total of 420 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Choose the correct choice from the following:
A) 648 B) 1800 C) 2800 D) 10800 E) 10900

Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 420 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 420 x = ( 10 x 4 x 420 ) / ( 6 ) x = 2800 . answer : c"
Answer: C