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 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>. What is the value of <math> \frac{A}{B}</math>? | + | Andy and Bethany have a rectangular array of numbers greater than zero 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 | ||
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==Solution== | ==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. | |
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==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=20|num-a=22}} | {{AMC8 box|year=2009|num-b=20|num-a=22}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 14:46, 6 January 2018
Problem
Andy and Bethany have a rectangular array of numbers greater than zero 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 |
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