Difference between revisions of "2009 AMC 8 Problems/Problem 24"
Mrdavid445 (talk | contribs) (Created page with "==Problem== The letters <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> represent digits. If <math> \begin{tabular}{ccc}&A&B\\ +&C&A\\ \hline &D&A\end{tabular...") |
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Now we can rewrite this as <math> \begin{tabular}{ccc}&5&0\\ +&C&5\\ \hline &D&5\end{tabular} </math>. Therefore, <math>D=5+C</math> | Now we can rewrite this as <math> \begin{tabular}{ccc}&5&0\\ +&C&5\\ \hline &D&5\end{tabular} </math>. Therefore, <math>D=5+C</math> | ||
| − | Finally, <math> A-1-C=0\implies{A=C+1}\implies{C=4} </math>, So we have <math> D=5+C\implies{D=5+4}=\boxed{9} </math> | + | Finally, <math> A-1-C=0\implies{A=C+1}\implies{C=4} </math>, So we have <math> D=5+C\implies{D=5+4}=\boxed{\textbf{(E)}\ 9 } </math> |
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2009|num-b=23|num-a=25}} | ||
Revision as of 16:46, 5 November 2012
Problem
The letters 
, 
, 
and 
represent digits. If 
and 
,what digit does represent?
Solution
Because 
, must be 
Next, because 
we get 
Now we can rewrite this as 
. Therefore, 
Finally, 
, So we have 
See Also
| 2009 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
