Difference between revisions of "2009 AMC 8 Problems/Problem 21"
Mrdavid445 (talk | contribs) (Created page with "==Problem== 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 <...") |
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\textbf{(D)}\ \frac{15}{8} \qquad | \textbf{(D)}\ \frac{15}{8} \qquad | ||
\textbf{(E)}\ \frac{225}{64}</math> | \textbf{(E)}\ \frac{225}{64}</math> | ||
| + | |||
| + | ==Solution== | ||
| + | Note that <math>40A=75B=\text{sum of the numbers in the array}</math>. This means that <math>\frac{A}{B}=\boxed{\text{(D) } \frac{15}{8}}</math> using basic algebraic manipulation. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2009|num-b=20|num-a=22}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 10:37, 16 January 2022
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 
. 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. 
