Question

-13 times the difference between a number and 60 is equal to the number plus -59

Answer 1

Let n represent the number.
-13×(n -60) = n +(-59)
-13n +780 = n -59
839 = 14n
839/14 = n = 59 13/14

The number is 59 13/14.

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Check
The difference between the number and 60 is
59 13/14 -60 = -1/14
-13 times that value is
-13*(-1/14) = 13/14
Compare that to the number plus -59
59 13/14 -59 = 13/14 . . . . . the same value, as required.