Difference between revisions of "1959 AHSME Problems/Problem 19"
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| + | == Problem == | ||
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With the use of three different weights, namely <math>1</math> lb., <math>3</math> lb., and <math>9</math> lb., how many objects of different weights can be weighed, if the objects is to be weighed and the given weights may be placed in either pan of the scale? <math>\textbf{(A)}\ 15 \qquad\textbf{(B)}\ 13\qquad\textbf{(C)}\ 11\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 7</math> | With the use of three different weights, namely <math>1</math> lb., <math>3</math> lb., and <math>9</math> lb., how many objects of different weights can be weighed, if the objects is to be weighed and the given weights may be placed in either pan of the scale? <math>\textbf{(A)}\ 15 \qquad\textbf{(B)}\ 13\qquad\textbf{(C)}\ 11\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 7</math> | ||
== Solution == | == Solution == | ||
| − | The heaviest object that could be weighed with this set weighs <math>1 + 3 + 9 = 13</math> lb., and we can weigh any positive integer weight at most that. This means that <math>13</math> different objects could be weighed, so our answer is <math>boxed{\textbf{(B)}}</math> and we are done. | + | The heaviest object that could be weighed with this set weighs <math>1 + 3 + 9 = 13</math> lb., and we can weigh any positive integer weight at most that. This means that <math>13</math> different objects could be weighed, so our answer is <math>\boxed{\textbf{(B)}}</math> and we are done. |
== See also == | == See also == | ||
Latest revision as of 12:59, 16 July 2024
Problem
With the use of three different weights, namely 
lb., 
lb., and 
lb., how many objects of different weights can be weighed, if the objects is to be weighed and the given weights may be placed in either pan of the scale? 
Solution
The heaviest object that could be weighed with this set weighs 
lb., and we can weigh any positive integer weight at most that. This means that 
different objects could be weighed, so our answer is 
and we are done.
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
