To find the lowest original score that will result in an A if the professor...

hexacordoK

hexacordoK

Answered

2021-03-05

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

Answer & Explanation

liannemdh

liannemdh

Expert

2021-03-06Added 106 answers

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+88=81.828
x=73.82
(ii) Consider (gf)(x)=1.1x+8
Plugging the final score of 90,
90=1.1x+8
Subtracting 8 from both the sides,
908=1.1x+88
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.

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