Difference between revisions of "2004 AMC 12B Problems/Problem 1"
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| − | ==Problem== | + | == Problem == |
| − | At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made | + | At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice? |
| − | <math>\mathrm{ | + | <math>(\mathrm {A}) 3\qquad (\mathrm {B}) 6 \qquad (\mathrm {C}) 9 \qquad (\mathrm {D}) 12 \qquad (\mathrm {E}) 15</math> |
| + | == Solution == | ||
| + | Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made <math>\frac{1}{2} \cdot 48 = 24</math> free throws, on the third <math>12</math>, on the second <math>6</math>, and on the first <math>3 \Rightarrow \mathrm{(A)}</math>. | ||
| − | + | Because there are five days, or four transformations between days (day 1 <math>\rightarrow</math> day 2 <math>\rightarrow</math> day 3 <math>\rightarrow</math> day 4 <math>\rightarrow</math> day 5), she makes <math>48 \cdot \frac{1}{2^4} = \boxed{\mathrm{(A)}\ 3}</math> | |
| − | + | ||
| + | |||
| + | == Video Solution 1== | ||
| + | https://youtu.be/6rkc-C9wllA | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| − | ==See Also== | + | == See Also == |
{{AMC12 box|year=2004|ab=B|before=First Question|num-a=2}} | {{AMC12 box|year=2004|ab=B|before=First Question|num-a=2}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 18:21, 22 October 2022
Contents
Problem
At each basketball practice last week, Jenny made twice as many free throws as she made at the previous practice. At her fifth practice she made 48 free throws. How many free throws did she make at the first practice?
Solution
Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made 
free throws, on the third 
, on the second 
, and on the first 
.
Because there are five days, or four transformations between days (day 1 
day 2 day 3 day 4 day 5), she makes 
Video Solution 1
~Education, the Study of Everything
See Also
| 2004 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by First Question |
Followed by Problem 2 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
