SOLUTION: One week, Mr. Slade promised to pay his son Joel $5 for each algebra problem he solved correctly. However, he would charge Joel $2 for each incorrect solution. At the end of the we

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Question 669852: One week, Mr. Slade promised to pay his son Joel $5 for each algebra problem he solved correctly. However, he would charge Joel $2 for each incorrect solution. At the end of the week Joel had completed 82 problems. Mr. Slade owes Joel $25. How many problems did Joel solve correctly.
I started by doing this but I cannot get an even number answer(C=Correct, I=Incorrect)
C+I=82
C(5)-I(2)=25
I=82-C
C(5)-(82-C)*2=25.
5C-(164-10C)=25
5C-164+10C=25
15C-164=25
+164 +164
15C=189
c=12.6
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the number of correct solutions
Let +i+ = the number of incorrect solutions
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+c+%2B+i+=+82+
+i+=+82+-+c+
+5c+-+2i++=+25+
+5c+-2%2A%28+82+-+c+%29+=+25+
+5c+-+164+%2B+2c+=+25+
+7c+=+189+
+c+=+27+
and
+i+=+82+-+c+
+i+=+82+-+27+
+i+=+55+
He solved 27 correctly
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Your mistake is the 6th line from the end
+10c+ should be +2c+