2020 AMC 10A Problems/Problem 9
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
.
Solution 2
This is similar to Solution 1, with the same basic idea, but we don't need to calculate the LCM. Since both and
are relatively prime, their LCM must be their product. So the answer would be
. ~Baolan
Video Solution
Education, The Study of Everything
~IceMatrix
~savannahsolver
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AMC 10 Problems and Solutions |
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