Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
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All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Answer:
580m^2
Step-by-step explanation:
600m^2 -20m=580m^2
Answer:
The value of given expression = - 5mx
Step-by-step explanation:
Given expression;
10xm - 8mx + 6xm - 13xm
Find:
The value of given expression
Computation:
⇒ 10xm - 8mx + 6xm - 13xm
Step 1 ;
Rearrange expression;
⇒ 10mx - 8mx + 6mx - 13mx
Step 2 ;
Adding all terms
⇒ 10mx + 6mx - 8mx - 13mx
Step 3 :
Subtract term
⇒ 16mx - 21mx
⇒ -5mx
The value of given expression = - 5mx
I can give you the answer only for the first question, but this one will definitely help you and bring you the points you need. The amount of tax that is paid on the computer is <span>0.08x, where </span>x is the original cost
and 8% is the tax rate. Hope you still need because that's really works.
Actually, 40 is divisible by 7. Any number is divisible by 7. However, 7 does not go into forty evenly. Your quotient would have a remainder since 7 cannot go into 40 an even number of times.
7 goes into 40 5 times evenly (7x5=35) 40-35 is five, so 40 divided by 7 is 5 (remainder 5)
~theLocoCoco
