# The sum of two consecutive numbers is 77. The difference of half of the smaller number and one-third of the larger number is 6. If x is the smaller number and y is the larger number, which two equations represent the sum and difference of the numbers?

$x + y = 77$
$\frac{1}{2} x - \frac{1}{3} y = 6$
$x = 38$
$y = 39$