Difference between revisions of "1999 AHSME Problems/Problem 11"
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| − | + | ==Problem== | |
| − | </math> \textbf{(A)}\ 2001 \qquad | + | The student locker numbers at Olympic High are numbered consecutively beginning with locker number <math> 1</math>. The plastic digits used to number the lockers cost two cents apiece. Thus, it costs two cents to label locker number <math> 9</math> and four centers to label locker number <math> 10</math>. If it costs $137.94 to label all the lockers, how many lockers are there at the school? |
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| + | <math> \textbf{(A)}\ 2001 \qquad | ||
\textbf{(B)}\ 2010 \qquad | \textbf{(B)}\ 2010 \qquad | ||
\textbf{(C)}\ 2100 \qquad | \textbf{(C)}\ 2100 \qquad | ||
\textbf{(D)}\ 2726 \qquad | \textbf{(D)}\ 2726 \qquad | ||
| − | \textbf{(E)}\ 6897 | + | \textbf{(E)}\ 6897</math> |
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| + | ==Solution 1== | ||
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| + | Since all answers are over <math>2000</math>, work backwards and find the cost of the first <math>1999</math> lockers. The first <math>9</math> lockers cost <math>0.18</math> dollars, while the next <math>90</math> lockers cost <math>0.04\cdot 90 = 3.60</math>. Lockers <math>100</math> through <math>999</math> cost <math>0.06\cdot 900 = 54.00</math>, and lockers <math>1000</math> through <math>1999</math> inclusive cost <math>0.08\cdot 1000 = 80.00</math>. | ||
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| + | This gives a total cost of <math>0.18 + 3.60 + 54.00 + 80.00 = 137.78</math>. There are <math>137.94 - 137.78 = 0.16</math> dollars left over, which is enough for <math>8</math> digits, or <math>2</math> more four digit lockers. These lockers are <math>2000</math> and <math>2001</math>, leading to answer <math> \boxed{\textbf{(A)}}</math>. | ||
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| + | ==See Also== | ||
| + | |||
| + | {{AHSME box|year=1999|num-b=10|num-a=12}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 06:19, 25 August 2024
Problem
The student locker numbers at Olympic High are numbered consecutively beginning with locker number 
. The plastic digits used to number the lockers cost two cents apiece. Thus, it costs two cents to label locker number 
and four centers to label locker number 
. If it costs $137.94 to label all the lockers, how many lockers are there at the school?
Solution 1
Since all answers are over 
, work backwards and find the cost of the first 
lockers. The first lockers cost 
dollars, while the next 
lockers cost 
. Lockers 
through 
cost 
, and lockers 
through inclusive cost 
.
This gives a total cost of 
. There are 
dollars left over, which is enough for 
digits, or 
more four digit lockers. These lockers are and 
, leading to answer 
.
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
