SOLUTION: can you help me solve this problem sir.... 1.) In order to encourage his son to study mathematics, a father agrees to pay his boy 50 centavos for every problem correctly solved, a

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Question 214345: can you help me solve this problem sir....
1.) In order to encourage his son to study mathematics, a father agrees to pay his boy 50 centavos for every problem correctly solved, and to fine him 25 centavos for each incorrect solution.At the end of 30 problems neither owed anything to the other.How many did the boy solved correctly?


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of problems solved correctly and y = the number of problems solved incorrectly.
We can express the problem algebraically in the two equations as:
1). 50x-25y+=+0 "...50 centavos for each problem correctly solved (x) and ...fine him 25 centavos for each incorrect solution (y)."
2). x%2By+=+30 The number of problems = 30. Rearrange this as: x+=+30-y and substitute into the first equation.
1a). 50%2830-y%29-25y+=+0 Simplify.
1b). 1500-50y-25y+=+0
1c). 1500-75y+=+0 Add 75y to both sides.
1d). 1500+=+75y Divide both sides by 75.
1e). 20+=+y and:
x+=+30-20
x+=+10
The boy solved 10 of the problems correctly.