1996 AHSME Problems/Problem 2
Problem
Each day Walter gets 
dollars for doing his chores or 
dollars for doing them exceptionally well. After 
days of doing his chores daily, Walter has received a total of 
dollars. On how many days did Walter do them exceptionally well?
Solution 1
If Walter had done his chores for days without doing any of them well, he would have earned 
dollars. He got 
dollars more than this.
He gets a 
dollar bonus every day he does his chores well. Thus, he did his chores exceptionally well 
days, and the answer is 
.
Solution 2
If Walter had done his chores for days exceptionally well, he would have earned 
dollars. He got 
dollars less than this.
He gets 
dollars docked from his pay if he doesn't do his chores well. Therefore, he didn't do his chores well on 
days. The other 
days, he did them exceptionally well. Therefore, the answer is .
Solution 3
Let 
be the number of days Walter does his chores but doesn't do them well, and let 
be the number of days he does his chores exceptionally well.
since there are days Walter does chores.
since 
is the amount he earns from doing his chores not well, and 
is the amount he earnes from doing his chores exceptionally well, and those two sum to dollars.
Multiply the first equation by to get:
Subtract the first equation from the second equation to get:
Thus, he does his chores well days, and the answer is .
See also
| 1996 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 3 | |
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