Difference between revisions of "2009 AMC 8 Problems/Problem 21"
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==Problem== | ==Problem== | ||
| − | Andy and Bethany have a rectangular array of numbers | + | Andy and Bethany have a rectangular array of numbers with <math> 40</math> rows and <math> 75</math> columns. Andy adds the numbers in each row. The average of his <math> 40</math> sums is <math> A</math>. Bethany adds the numbers in each column. The average of her <math> 75</math> sums is <math> B</math>. Using only the answer choices given, What is the value of <math> \frac{A}{B}</math>? |
<math> \textbf{(A)}\ \frac{64}{225} \qquad | <math> \textbf{(A)}\ \frac{64}{225} \qquad | ||
Revision as of 16:42, 22 December 2021
Problem
Andy and Bethany have a rectangular array of numbers with 
rows and 
columns. Andy adds the numbers in each row. The average of his sums is 
. Bethany adds the numbers in each column. The average of her sums is 
. Using only the answer choices given, What is the value of 
?
Solution
Note that 
. This means that 
using basic algebraic manipulation.
See Also
| 2009 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
