Answer:
(a) 20%
Step-by-step explanation:
The percent increase is found from ...
% change = ((new) -(original))/(original) × 100%
= (90 -75)/75 × 100% = 15/75 × 100%
% change = 20%
The student's grade average increased by 20% of what it was.
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Additional comment
The student's grade average went up by 90-75 = 15 (points). These are often percentage points, so we could say the grade average increased by 15 percentage points.
The important point here is to be clear on what the basis is for computing a percentage change. If a score of 75 is the basis, then a change to a score of 90 is a change of 20% of that original score of 75.
If the maximum possible grade points are the basis, then a change from 75% of maximum to 90% of maximum is an increase of 15% of that maximum.
The wording here, "percent of increase in the student's grade average" suggests that the original grade average is the basis for measuring the change.
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You often see (intentional) confusion of the basis in media reports. If violent crime, for example, increases from 2% of all crime to 3% of all crime, the media may claim a 50% increase in the rate of violent crime. On the other hand, it could be considered to be a 1% increase (3% -2% = 1%). If the relative increase is due to a large reduction in all crime, the actual amount of violent crime may have decreased. (2/100 = 2%; 1/33 = 3%) The numbers chosen will depend on who is reporting and what the purpose of the report is.
