SOLUTION: there are 26 problems on a test. The boys father offers $8.00 for each correct answer and will take away $5.00 for each incorrect answer. At the end of the test they don't owe ea

Question 167009: there are 26 problems on a test. The boys father offers $8.00 for each correct answer and will take away $5.00 for each incorrect answer. At the end of the test they don't owe each other any money. How many questions did the boy answer correctlY.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the number of correctly-answered problems and y = the number of incorrectly-answered problems.
The sum of these is given as 26 (x+y = 26), the total number of problems on the test.
Foe each correct answer, the son gets $8.00 for a total of x($8.00).
For each incorrect answer, the son loses $5.00 for a total of -y($5.00).
In the end, these two ampounts must be equal since neither one owes the other anything, so...
x($8.00)-y($5.00) = 0 From (x+y = 26), substitute: y = 26-x.
(8)(x)-(5)(26-x) = 0 Simplify.
8x-130+5x = 0
13x-130 = 0
13x = 130
x = 10 and y = 16
The boy answered 10 questions correctly.

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