Let H be the number of hamburgers sold and C be the number of cheeseburgers sold.
The total number of hamburgers and cheeseburgers sold is given by the equation: H + C = 429
The number of cheeseburgers sold is given by the equation: C = 2H
Substituting the second equation into the first equation, we get: H + 2H = 429
Combining like terms, we get: 3H = 429
Dividing both sides by 3, we get: H = 143
On Thursday, 143 hamburgers were sold.