The sum of two numbers is 80. The larger number is four more than three times the smaller number. Find both numbers.

Let the smaller number = X

Then the larger number is 3x+4 (four more than 3 times the smaller number)

The sum of both numbers = 80

so you have X + 3X+4 = 80

Simplify the left side:

4x+4 = 80

Subtract 4 from each side:

4x = 76

Divide both sides by 4:

X = 76/4

X = 19

The smallest number is 19

The largest number is 80 - 19 = 61 (check: 3*19 = 57+4 = 61)

The two numbers are 19 and 61