SOLUTION: 3. To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect so

Question 527491: 3. To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect solution. At the end of the first 26 problems of the problem set, neither owed any money to the other. How many problems did the daughter solve correctly?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect solution. At the end of the first 26 problems of the problem set, neither owed any money to the other. How many problems did the daughter solve correctly?
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Expected Value:
8c - 5w = 0 dollars
c + w = 26 problems
------
Multiply thru the 2nd equation by 5:
8c - 5w = 0
5c + 5w = 5*26
---
Add to get:
13c = 5*26
c = 10 (# of questions answered correctly)
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Cheers,
Stan H.
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Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of correct solutions
Let = number of incorrect solutions
given:
(1)
(2)
------------
Multiply both sides of (2) by
and add the equations
(1)
(2)

and, since
(2)
(2)
(2)
The daughter solved 10 equations correctly
check:
(1)
(1)
(1)

OK
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