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?

X = 29 + 3y

5 (x-y) = 345

5x-5y = 345

5 (29+3y) - 5y = 345

145 + 15y-5y = 345

10y + 145-145 = 345-145

10y = 200

y = 20

x = 29 + 3y = 29 + 3 (20) = 29 + 60 = 89

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.