Difference between revisions of "2009 AMC 10A Problems/Problem 8"
(New page: A senior ticket costs <dollar/><math>6.00</math>, so a regular ticket costs <math>6 * \frac{1}{\frac{3}{4}}\:=\:6*\frac{4}{3}\:=\:8</math> dollars. Therefore children's tickets cost half t...) |
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− | + | == 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 <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> | ||
+ | \mathrm{(A)}\ 34 | ||
+ | \qquad | ||
+ | \mathrm{(B)}\ 36 | ||
+ | \qquad | ||
+ | \mathrm{(C)}\ 42 | ||
+ | \qquad | ||
+ | \mathrm{(D)}\ 46 | ||
+ | \qquad | ||
+ | \mathrm{(E)}\ 48 | ||
+ | </math> | ||
+ | |||
+ | == Solution == | ||
+ | |||
+ | 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 < | + | So Grandfather Wen pays <math>$36</math>, or <math>\fbox{B}</math>. |
+ | |||
+ | ==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 == | ||
+ | |||
+ | {{AMC10 box|year=2009|ab=A|num-b=7|num-a=9}} | ||
+ | {{MAA Notice}} |
Latest revision as of 15:53, 28 July 2023
Contents
[hide]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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