smc

Question

The student locker numbers at Olympic High are numbered consecutively beginning with locker number 1. The plastic digits used to number the lockers cost two cents apiece. Thus, it costs two cents to label locker number 9 and four centers to label locker number 10. If it costs $137.94 to label all the lockers, how many lockers are there at the school?

Accepted Answer

Since all answers are over 2000, work backwards and find the cost of the first 1999 lockers. The first 9 lockers cost 0.18 dollars, while the next 90 lockers cost 0.04 90 = 3.60. Lockers 100 through 999 cost 0.06 900 = 54.00, and lockers 1000 through 1999 inclusive cost 0.08 1000 = 80.00. This gives a total cost of 0.18 + 3.60 + 54.00 + 80.00 = 137.78. There are 137.94 - 137.78 = 0.16 dollars left over, which is enough for 8 digits, or 2 more four digit lockers. These lockers are 2000 and 2001, leading to answer 2001.