C hina and the United States both paid a heavy price for their mutual hostility lasting 23 years from 1949 to 1971. China and the United States both paid heavy prices for their mutual hostility lasting 23 years from 1949 to 1971. You are logically correct unless the price is precisely the same, but the first form is nevertheless common and quite understandable.
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AnonymousI think it should be "China and United states both paid heavy prices ...Not idiomatic in my opinion. 'both' can be taken as 'each', so there's no need to be so fastidious about this.