Difference between revisions of "2001 AMC 10 Problems/Problem 8"
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Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab? | Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab? | ||
| − | <math> \textbf{(A) }42\qquad\textbf{(B) }84\qquad\textbf{(C) }126\qquad\textbf{(D) }178\qquad\textbf{(E) }252 </math> | + | <math> \textbf{(A) }42\qquad\textbf{(B) }84\qquad\textbf{(C) }126\qquad\textbf{(D) }178\qquad\textbf{(E) }252</math> |
== Solution == | == Solution == | ||
| − | + | By translating the words in the problem into the language of mathematics, the problem is telling us to find the least common multiple of the four numbers given. | |
| − | |||
| − | <math> 3 \ | + | <math>\textrm{LCM}(3, 4, 6, 7) = \textrm{LCM}(3, 2^2, 2 \cdot 3, 7) = 2^2 \cdot 3 \cdot 7 = 84</math> |
| − | + | So the answer is <math>\boxed{\textbf{(B) } 84} </math>. | |
| − | + | ==Video Solution by Daily Dose of Math== | |
| − | + | https://youtu.be/ts2x9Q0XVM0?si=uxpzYXU3VacX2lKm | |
| + | |||
| + | ~Thesmartgreekmathdude | ||
== See Also == | == See Also == | ||
{{AMC10 box|year=2001|num-b=7|num-a=9}} | {{AMC10 box|year=2001|num-b=7|num-a=9}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 21:30, 13 August 2024
Problem
Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?
Solution
By translating the words in the problem into the language of mathematics, the problem is telling us to find the least common multiple of the four numbers given.
So the answer is 
.
Video Solution by Daily Dose of Math
https://youtu.be/ts2x9Q0XVM0?si=uxpzYXU3VacX2lKm
~Thesmartgreekmathdude
See Also
| 2001 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
