document.write( "Question 553034: In order to encourage his son to study arithmetic, a father agrees to pay his boy $8 for every problem correctly solved and to fine him $5 for each incorrect solution. At the end of 26 problems, neither owes anything to the other. How many problems did the boy solve correctly \n" ); document.write( "
Algebra.Com's Answer #360685 by htmentor(1343)\"\" \"About 
You can put this solution on YOUR website!
In order to encourage his son to study arithmetic, a father agrees to pay his boy $8 for every problem correctly solved and to fine him $5 for each incorrect solution. At the end of 26 problems, neither owes anything to the other. How many problems did the boy solve correctly
\n" ); document.write( "=============================
\n" ); document.write( "Let c = the number of correct problems
\n" ); document.write( "Let w = the number of wrong problems
\n" ); document.write( "At the end of 26 problems, the boy does not owe anything:
\n" ); document.write( "8c - 5w = 0
\n" ); document.write( "And since the total number is 26, the sum of the correct and incorrect problems totals 26:
\n" ); document.write( "c + w = 26
\n" ); document.write( "Solve for w in the 2nd equation and substitute in the 1st:
\n" ); document.write( "8c - 5(26-c) = 0
\n" ); document.write( "13c = 130
\n" ); document.write( "c = 10
\n" ); document.write( "So the boy solved 10 problems correctly
\n" ); document.write( "Check:
\n" ); document.write( "10*8 - 16*5 = 0 = 80 - 80 \n" ); document.write( "
\n" );