Question 1112557

perfect score in math is 200.
perfect score in science is 150
perfect score in social studies is 150
perfect score in language is 100.


90% in math = .9 * 200 = 180.
85% in science = .85 * 150 = 127.5
80% in social studies = .8 * 150 = 120
75% in language = .75 * 100 = 75


total score is 180 + 127.5 + 120 + 75 = 502.5 out of a possible 200 + 150 + 150 + 100 = 600


502.5 / 600 = .8375 = 83.75%


to improve this by 20%, he will need to get an overall aggregate percentage of 1.2 * 83.75% = 100.5%.


he cannot improve his overall percentage by 20% because that would give him a score that is over 100%.


if he improved his language scores by 20%, then he would get 90 right instead of 75.


that would be an improvement of 15 points.


his overall score would then be 502.5 + 15 = 517.5.


his overall percentage would then be 517.5 / 600 = .8625 which is equal to 86.25%.


the increase in his overall percentage would be 86.25% minus 83.75% = 2.5%.


this represents a percent increase of 2.5% / 83.75% = .0298507463 = 2.98507463% over his original overall percentage.


his original percent was 502.5/600 = .8375 = 83.75%


his new percent would be 517.5/600 = .8625 = 86.25%.