Difference between revisions of "2010 AMC 10B Problems/Problem 9"
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<math>-e-2</math> | <math>-e-2</math> | ||
| − | Therefore we have the equation <math>e-8=-e-2\implies 2e=6\implies e=3 \Rightarrow \boxed{ | + | Therefore we have the equation <math>e-8=-e-2\implies 2e=6\implies e=3 \Rightarrow \boxed{D}</math> |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2010|ab=B|num-b=8|num-a=10}} | {{AMC10 box|year=2010|ab=B|num-b=8|num-a=10}} | ||
Revision as of 16:24, 6 September 2011
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 sustitued for , , , and were 
, 
, 
, and 
, respectively. What number did Larry substitude for ?
Solution
Solution 1
Simplify the expression . I recommend to start with the innermost parenthesis and work your way out.
So you get:
Henry substituted 
with 
respectively.
We have to find the value of , such that 
(the same expression without parenthesis).
Substituting and simplifying we get:
So Henry must have used the value for .
Our answer is 
Solution 2
Lucky Larry had not been aware of the parenthesis and would have done the following operations:
The correct way he should have done the operations is:
Therefore we have the equation 
See Also
| 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 | ||
