Difference between revisions of "2020 AMC 10A Problems/Problem 9"
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A single bench section at a school event can hold either <math>7</math> adults or <math>11</math> children. When <math>N</math> bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of <math>N?</math> | A single bench section at a school event can hold either <math>7</math> adults or <math>11</math> children. When <math>N</math> bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of <math>N?</math> | ||
Revision as of 22:46, 31 January 2020
Problem
A single bench section at a school event can hold either 
adults or 
children. When 
bench sections are connected end to end, an equal number of adults and children seated together will occupy all the bench space. What is the least possible positive integer value of 
Solution
The least common multiple of and is 
. Therefore, there must be adults and children. The total number of benches is 
.
See Also
| 2020 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
