Difference between revisions of "2010 AMC 12B Problems/Problem 5"
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| − | == Problem | + | == Problem == |
| − | Lucky Larry's teacher asked him to substitute numbers for <math>a</math>, <math>b</math>, <math>c</math>, <math>d</math>, and <math>e</math> in the expression <math>a-(b-(c-(d+e)))</math> and evaluate the result. Larry ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry | + | Lucky Larry's teacher asked him to substitute numbers for <math>a</math>, <math>b</math>, <math>c</math>, <math>d</math>, and <math>e</math> in the expression <math>a-(b-(c-(d+e)))</math> and evaluate the result. Larry ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> were <math>1</math>, <math>2</math>, <math>3</math>, and <math>4</math>, respectively. What number did Larry substitute for <math>e</math>? |
<math>\textbf{(A)}\ -5 \qquad \textbf{(B)}\ -3 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 5</math> | <math>\textbf{(A)}\ -5 \qquad \textbf{(B)}\ -3 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 5</math> | ||
| Line 9: | Line 9: | ||
<cmath>-8 + e = -2 - e</cmath> | <cmath>-8 + e = -2 - e</cmath> | ||
<cmath>2e = 6</cmath> | <cmath>2e = 6</cmath> | ||
| − | <cmath>e = 3</cmath> | + | <cmath>e = 3 \;\;(D)</cmath> |
| − | + | ||
| + | ==Video Solution== | ||
| + | https://youtu.be/OiJ-9eGCLGM | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/I3yihAO87CE?t=303 | ||
| + | |||
| + | ~IceMatrix | ||
== See also == | == See also == | ||
| − | {{AMC12 box|year=2010|num-b= | + | {{AMC12 box|year=2010|num-b=4|num-a=6|ab=B}} |
| + | {{AMC10 box|year=2010|num-b=8|num-a=10|ab=B}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:02, 1 August 2022
Problem
Lucky Larry's teacher asked him to substitute numbers for 
, 
, 
, 
, and 
in the expression 
and evaluate the result. Larry ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry substituted for , , , and were 
, 
, 
, and 
, respectively. What number did Larry substitute for ?
Solution
We simply plug in the numbers
![\[1 - 2 - 3 - 4 + e = 1 - (2 - (3 - (4 + e)))\]](http://latex.artofproblemsolving.com/7/a/4/7a45109237a44425ac1f654e545592212c0e8d24.png)
![\[-8 + e = -2 - e\]](http://latex.artofproblemsolving.com/6/4/0/6404d113e89d63c3e63dc55c338e718f1b906f27.png)
![\[2e = 6\]](http://latex.artofproblemsolving.com/f/5/4/f5474d53aa43904dd17b97dc61e0d5e8d8c333fb.png)
![\[e = 3 \;\;(D)\]](http://latex.artofproblemsolving.com/3/0/b/30b7a727bd9caf1881ba760eb4c0986ba4c340b4.png)
Video Solution
~Education, the Study of Everything
Video Solution
https://youtu.be/I3yihAO87CE?t=303
~IceMatrix
See also
| 2010 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 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 | |
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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. 
