2009 AMC 10A Problems/Problem 8
Contents
Problem 8
Three Generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a 
% discount as children. The two members of the oldest generation receive a 
discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs 
, is paying for everyone. How many dollars must he pay?
Solution
A senior ticket costs , so a regular ticket costs 
dollars. Therefore children's tickets cost half that, or 
, so we have:
So Grandfather Wen pays 
, or 
.
Solution 2
Using average, we know that assuming the middle-aged people's ticket cost x dollars, $2\cdot(100%x+75%x+50%x).$ (Error compiling LaTeX. Unknown error_msg) We average this into $2\cdot(75%x+75%x+75%x).$ (Error compiling LaTeX. Unknown error_msg) We know that 75%x=6.00, which means 6*6 is the answer, or 36. -RealityWrites
See Also
| 2009 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 AMC 10 Problems and Solutions | ||
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