# 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 coll

To find the lowest original score that will result in an A if the professor uses
$$(i)(f \times g)(x)\ and\ (ii)(g \times f)(x)$$.
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.
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student

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liannemdh

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