Question

Two numbers have a sum of 24 and 7 times the first number minus the second number is equal to 16. what is the smaller number

Answer 1

You want the minimum of the solutions to
  x + y = 24
  7x - y = 16

There are many ways to solve these equations. Adding them together, you get
  8x = 40
  x = 5

Since this value is less than 12, it is the smaller number. The smaller number is 5.