The difference between two numbers is 53. five times the smaller is equal to 3 more than larger. what are the numbers?

First, let's assign two variables: one for the bigger one, and one for the smaller one. The smaller number will be represented as 's,' and the bigger one will be 'b.'

Since their difference is 53, we can make an equation:
b - s = 53

Since 5 times the smaller is equal to 3 times the bigger, we can make one more equation:
5s = 3b

We can divide both sides by 5 to simplify this equation:
s = 3b/5

Input this value of 's' into our first equation:
b - (3b/5) = 53

In order to get rid of that pesky denominator, multiply everything by 5:
5b - 3b = 265
2b = 265

b = 132.5
Input this into our first equation to find the smaller number:
s = (3*132.5)/5
s = 79.5

The two numbers are 132.5 and 79.5
-T.B.