SOLUTION: Suppose that I agree to pay you .08 cents for every problem you solve correctly on a test and fine you .05 cents for for every problem that you get wrong. If at the end of 26 probl

Question 2520: Suppose that I agree to pay you .08 cents for every problem you solve correctly on a test and fine you .05 cents for for every problem that you get wrong. If at the end of 26 problems we do not owe each other any money, how many problems did you get right?
Answer by kiru_khandelwal(79) (Show Source): You can put this solution on YOUR website!
Suppose that total problem solved correctly be x and that done incorrectly be y
as total 26 problems are done
x+y = 26 ...........Equation(1)
.08 cents is paid for each right answer
so for x correct answers total amount paid will be .08x
.05 cents are fined for each incorrect answer
so for y incorrect answers total amount fined will be .05y
Now at the end of 26 problems no money is owed by neone...this means the amount to be paid and to be fined are equal
=> .08x = .05y
=> .08x -.05y = 0
=> (8/100)x - (5/100)y = 0
=> (8x-5y)/100 = 0
=> 8x-5y = 0
=> 8x = 5y
=> x = 5y/8............equation(2)
substituting the value of x from equation(2) to equation(1)
x+y = 26
=> 5y/8 + y = 26
=> 13y/8 = 26
=> 13y = 26*8
=> y = 16
so x= 10
No. of problems done right is 10
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