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 == | == Solution == | ||
| − | A senior ticket costs | + | A senior ticket costs <math>\$6.00</math>, so a regular ticket costs <math>6 \cdot \frac{1}{\frac{3}{4}}\:=\:6\cdot\frac{4}{3}\:=\:8</math> dollars. Therefore children's tickets cost half that, or <math>\$4.00</math>, so we have: |
<math>2(6+8+4)\:=\:36</math> | <math>2(6+8+4)\:=\:36</math> | ||
| − | So Grandfather Wen pays <math>\$36</math>, or <math>B</math>. | + | So Grandfather Wen pays <math>\$36</math>, or <math>\fbox{B}</math>. |
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| + | ==Solution 2== | ||
| + | Using average, we know that assuming the middle-aged people's ticket cost x dollars, <math>2\cdot(100\%x+75\%x+50\%x)</math>. 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 15:53, 28 July 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, 
. 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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