Difference between revisions of "2001 AMC 12 Problems/Problem 1"
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| + | {{duplicate|[[2001 AMC 12 Problems|2001 AMC 12 #1]] and [[2001 AMC 10 Problems|2001 AMC 10 #3]]}} | ||
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== Problem == | == Problem == | ||
The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number and then | The sum of two numbers is <math>S</math>. Suppose <math>3</math> is added to each number and then | ||
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numbers? | numbers? | ||
| − | <math>\ | + | <math>\textbf{(A)}\ 2S + 3\qquad \textbf{(B)}\ 3S + 2\qquad \textbf{(C)}\ 3S + 6 \qquad\textbf{(D)}\ 2S + 6 \qquad \textbf{(E)}\ 2S + 12</math> |
== Solution == | == Solution == | ||
Suppose the two numbers are <math>a</math> and <math>b</math>, with <math>a+b=S</math>. | Suppose the two numbers are <math>a</math> and <math>b</math>, with <math>a+b=S</math>. | ||
Then the desired sum is | Then the desired sum is | ||
| − | <math>2(a+3)+2(b+3)=2(a+b)+12=2S +12</math>, which is answer <math>\ | + | <math>2(a+3)+2(b+3)=2(a+b)+12=2S +12</math>, which is answer <math>\boxed{\textbf{(E)}}</math>. |
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| + | ==Video Solution by Daily Dose of Math== | ||
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| + | https://youtu.be/FxFb_QALttI?si=qUQVUkuBeK1cRbtS | ||
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| + | ~Thesmartgreekmathdude | ||
== See also == | == See also == | ||
{{AMC12 box|year=2001|before=First question|num-a=2}} | {{AMC12 box|year=2001|before=First question|num-a=2}} | ||
{{AMC10 box|year=2001|num-b=2|num-a=4}} | {{AMC10 box|year=2001|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 15:10, 15 July 2024
- The following problem is from both the 2001 AMC 12 #1 and 2001 AMC 10 #3, so both problems redirect to this page.
Problem
The sum of two numbers is 
. Suppose 
is added to each number and then
each of the resulting numbers is doubled. What is the sum of the final two
numbers?
Solution
Suppose the two numbers are 
and 
, with 
.
Then the desired sum is
, which is answer 
.
Video Solution by Daily Dose of Math
https://youtu.be/FxFb_QALttI?si=qUQVUkuBeK1cRbtS
~Thesmartgreekmathdude
See also
| 2001 AMC 12 (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 | |
| 2001 AMC 10 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
