Let the number of apartments be x. We know that the cost of the digits is $1 each, and that the total cost of the digits is $282. Therefore, we can set up the following equation:
1x + 1(x+1) + 1(x+2) + ... + 1(x+(n-1)) = 282
Simplifying this equation, we get:
nx + n(n-1)/2 = 282
We can solve for n using the quadratic formula:
n = (-1 ± sqrt(1 + 4(2*282)))/2
n = 21.06 or n = -20.06
Since the number of apartments must be a positive integer, we can round up to the nearest integer, giving us n = 22. Therefore, Tabitha will be numbering 22 apartments.
Extra: On Monday, the store sells 1s for half price, or $0.50. This means that the total cost of the digits would be:
1x + 0.5(x+1) + 0.5(x+2) + ... + 0.5(x+(n-1)) = 141
Simplifying this equation, we get:
nx + n(n-1)/4 = 141
Using the quadratic formula again, we get:
n = (-1 ± sqrt(1 + 4(4*141)))/2
n = 16.76 or n = -15.76
Rounding up to the nearest integer, we get n = 17. Therefore, if Tabitha had bought the digits on Monday, she could have saved 5 digits, or $5.