Difference between revisions of "2009 AMC 10A Problems/Problem 8"
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== Problem 8 == | == Problem 8 == | ||
− | Three | + | Three generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a <math>50</math>% discount as children. The two members of the oldest generation receive a <math>25\%</math> discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs <math>\$6.00</math>, is paying for everyone. How many dollars must he pay? |
<math> | <math> | ||
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==Solution 2== | ==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). We average this into 2*(75%x+75%x+75%x). We know that 75%x=6.00, which means <math>6\cdot6</math> is the answer, or 36. -RealityWrites | ||
== See Also == | == See Also == |
Latest revision as of 00:18, 20 February 2023
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). We average this into 2*(75%x+75%x+75%x). We know that 75%x=6.00, which means 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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