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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

A public school teacher has graded 25 papers and has found that the average grade is 65.5 points out of 100 points possible. Since the passing grade is 51%, the teacher has decided to raise 15 of the grades by 1 point and thus make sure that more students pass and move on to another teacher's class. What is the new grade average after this raise?

The average A of the grades is the sum S of all the grades divided by the number of grades:

equation

The sum of the grades is:

equation

By adding 1 to 15 of the grades, the teacher increased the sum of all the grades by 15:

equation

The new average is:

equation