To find the lowest original score that will result in an A if the professor uses (i)(f×g)(x) and (ii)(g×f)(x). Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test. One problem worth 8 points had insufficient data, so nobody could solve that problem. The professor adjusted the grades for the class by a. Increasing everyone's score by 10% and b. Giving everyone 8 bonus points c. x represents the original score of a student

Question

To find the lowest original score that will result in an A if the professor uses (i)(f×g)(x) and (ii)(g×f)(x). Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test. One problem worth 8 points had insufficient data, so nobody could solve that problem. The professor adjusted the grades for the class by a. Increasing everyone&#039;s score by 10% and b. Giving everyone 8 bonus points c. x represents the original score of a student

liannemdh · Accepted Answer

The function f(x)=1.1 xrepresents the score increased by 10% The function g(x)=x+8 represents the score increased by 8 points The function (f×g)(x)=1.1(x+8) represents the final score when the score is first increased by 8 bonus points and then by 10% The function (g×f)(x)=l.lx+8 represents the final score when the score is first increased by 10% and then by 8 bonus points A score of 90 or better results in an A Calculation: (i) Consider (f×g)(x)=1.1(x+8) Plugging the final score of 90, 90=1.1(x+8) Dividing by 1.1 on both the sides, 901.1=1.1(x+8)1.1 81.8181...=x+8 x+8=818181... x+8=81.82 Subtracting 8 from both the sides, x+8−8=81.82−8 x=73.82 (ii) Consider (g⋅f)(x)=1.1x+8 Plugging the final score of 90, 90=1.1x+8 Subtracting 8 from both the sides, 90−8=1.1x+8−8 82=1.1x 1.1x=82 Dividing by 1.1 on both the sides, 1.1x1.1=821.1 x=74.5454... x=74.55.