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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| − | A senior ticket costs <dollar/><math>6.00</math>, so a regular ticket costs <math>6 | + | == 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 <dollar/><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 <dollar/><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 <dollar/><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 <dollar/><math>36</math>, or <math>B</math>. | So Grandfather Wen pays <dollar/><math>36</math>, or <math>B</math>. | ||
| + | |||
| + | == See Also == | ||
| + | |||
| + | {{AMC10 box|year=2009|ab=A|num-b=7|num-a=9}} | ||
Revision as of 03:57, 13 February 2009
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 <dollar/>
, is paying for everyone. How many dollars must he pay?
Solution
A senior ticket costs <dollar/>, so a regular ticket costs 
dollars. Therefore children's tickets cost half that, or <dollar/>
, so we have:
So Grandfather Wen pays <dollar/>
, or 
.
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 | ||
