During a school year, a student was given an award of 25¢ for each math test he passed and was fined 50¢ for each math test he failed. At the end of the school year, the student had passed 7 times as many tests as he had failed, and received $3.75. How many tests did he fail?
Let P be the number of tests the student passed and F be the number of tests the student failed.
As the student has passed 7 times as many tests as he had failed,
P = 7F ------(1)
As he has received a total of $3.75 = 375¢
25P - 50F = 375 -------(2)
Substituting for P in eqn(2)
25 * 7F - 50F = 375
175F - 50F = 375
125F = 375
F = 3
The student failed in 3 tests.
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