The sum of two numbers is 24. If 4 less than 6 times the smaller number equals 5 more than 3 times the larger, what are the numbers?

Let x = smaller number, y = larger number

The first statement is expressed as

x + y = 24

The second statement is expressed as

6x - 4 = 3y + 5

Solving for x by substituting the first equation of terms of y which is y = 24 - x,

6x - 4 = 3 (24 - x) + 5

6x - 4 = 72 - 3x + 5

6x + 3x = 72 + 5 + 4

9x = 81

x = 81/9 = 9

Solving for y,

y = 24 - 9 = 15

So the numbers are 9 and 15.