 hexacordoK

2021-03-05

To find the lowest original score that will result in an A if the professor uses
.
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.
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student liannemdh

Expert

The function $f\left(x\right)=1.1$ xrepresents the score increased by 10%
The function $g\left(x\right)=x+8$ represents the score increased by 8 points
The function $\left(f×g\right)\left(x\right)=1.1\left(x+8\right)$ represents the final score when the score is first increased by 8 bonus points and then by 10%
The function $\left(g×f\right)\left(x\right)=l.lx+8$ 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 $\left(f×g\right)\left(x\right)=1.1\left(x+8\right)$
Plugging the final score of 90,
$90=1.1\left(x+8\right)$
Dividing by 1.1 on both the sides,
$\frac{90}{1.1}=\frac{1.1\left(x+8\right)}{1.1}$
$81.8181...=x+8$
$x+8=818181...$
$x+8=81.82$
Subtracting 8 from both the sides,
$x+8-8=81.82-8$
$x=73.82$
(ii) Consider $\left(g\cdot f\right)\left(x\right)=1.1x+8$
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,
$\frac{1.1x}{1.1}=\frac{82}{1.1}$
$x=74.5454...$
$x=74.55$.

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