One number is twenty-nine more than three times another number. if each number were multiplied by five. their difference would be 345. what are the numbers?

Let the two numbers be represented by x and y.
.. y = 29 +3x
.. 5(y -x) = 345
From the second equation,
.. y -x = 345/5 = 69
Substituting for y in the first, we have
.. 69 +x = 29 +3x
.. 40 = 2x
.. x = 20
Then
.. y = 29 +3*20 = 89

The two numbers are 89 and 20.