Thirteen plums weigh as much as two apples and one pear. Four plums and one apple have the same weight as one pear. How many plums have the same weight as one pear?

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Let U be plums, A be apples and P be pears.

13U = 2A + P

4U + A = P

Substituting P from the second equation to the first:

13U = 2A + 4U + A

9U = 3A

A = 3U

Now, substituting the value of A into the second equation:

4U + 3U = P

7U = P

7 plums weigh the same as one pear.