Peter watches 805 American movies and 460 Chinese movies.
Let x represent the number of American movies and y represent the number of Chinese movies and let z represent the total number of movies.
Since he watches 345 more American movies than Chinese movies. Hence:
x = y + 345
x - y = 345 (1)
Also:
x + y = z
x + y - z = 0 (2)
The ratio of Chinese movies to American movies is 4:7. Hence:
(4/11)z = y
-y + (4/11)z = 0 (3)
Solving equations 1, 2, and 3, simultaneously gives:
x = 805, y = 460 and z = 1265
Hence, Peter watches 805 American movies and 460 Chinese movies.
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