1999 AHSME Problems/Problem 11

Problem

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?

$\textbf{(A)}\ 2001 \qquad \textbf{(B)}\ 2010 \qquad \textbf{(C)}\ 2100 \qquad \textbf{(D)}\ 2726 \qquad \textbf{(E)}\ 6897$

Solution 1

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 $0.04\cdot 90 = 3.60$ . Lockers $100$ through $999$ cost $0.06\cdot 900 = 54.00$ , and lockers $1000$ through $1999$ inclusive cost $0.08\cdot 1000 = 80.00$ .

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 $\boxed{\textbf{(A)}}$ .

1999 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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1999 AHSME Problems/Problem 11

Problem

Solution 1

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