0

I know the answer is probably very basic math, but I can't seem to figure it out. I want a 92 overall grade in math.

-Test scores (make up 60% of grade): 86, 91, 90, 89

-Quiz scores (make up 25% of grade): 95, 91, 83, 89

-Homework (make up 15% of grade): 100, 91, 85, 90

How would I calculate what I need to score on my next test to achieve a 92 or greater grade?

nmares12
  • 15
  • 1
  • 1
  • 5
  • Very similar questions: http://math.stackexchange.com/questions/748319/solving-minumum-needed-to-acheive-a-final-grade-of-85?rq=1 and http://math.stackexchange.com/questions/1213042/how-to-calculate-what-i-need-for-final-exam?rq=1 and http://math.stackexchange.com/questions/1290247/i-need-a-mathematical-percentage-for-a-final-exam-grade-too-see-how-many-points?rq=1 – David K Jul 06 '15 at 21:43

2 Answers2

0

The requirement on the total score $S$ depending on the scores $T$, $Q$ and $H$ is: $$ S = \frac{60 T + 25 Q + 15 H}{100} \ge 92 $$

The rest is systematic trial of the $4^3$ combinations.

mvw
  • 34,562
0

The average for each category (test, quiz, homework) is weighted as prescribed. So just give a name to your unknown test score and write an equation stating that the weighted average should be equal to your desired grade, and solve it for the unknown.

Let $x$ be the score on the 5th test. Then the overall grade after taking the 5th test is

$$0.60(\overbrace{\tfrac{86+91+90+89+x}{5}}^{\textrm{test average}}) + 0.25(\overbrace{\tfrac{95+91+83+89}{4}}^{\textrm{quiz average}}) + 0.15(\overbrace{\tfrac{100+91+85+90}{4}}^{\textrm{homework average}})$$

$$0.60(\tfrac{356+x}5) + 0.25(\tfrac{358}{4}) + 0.15(\tfrac{366}4) $$ $$0.60(\tfrac{356}5 +\tfrac15x) + 0.25(89.5) + 0.15(91.5)$$ $$0.60(71.2) +0.60(\underbrace{0.2}_{1/5})x + 0.25(89.5)+0.15(91.5)$$ $$42.72 + 0.12x + 22.375 + 13.725$$ $$78.82+0.12x$$ Then the equation you have to solve to for the score that gives you exactly a 92 average is $$78.82 + 0.12 x = 92$$ $$0.12x = 92-78.82$$ $$0.12x = 13.18$$ $$x = \frac{13.18}{0.12} = 109.8\bar{3}$$ A higher score will produce a higher average, and a lower score will produce a lower average.

Unless it is possible to earn a score of at least $109.8\bar{3}$, you can't reach the desired target with just this single test score. Additional tests/homeworks/quizzes may make it possible.

Addendum: The work above can be slightly generalized. Instead of using $92$, suppose your target grade is $g$. Then the equation to solve would be

$$78.82 + 0.12 x = g$$ $$x = \frac{g - 78.82}{0.12}$$

This tells you, for example, that to end up with an average of $78.82$, you would have to make at least a $0$ on the 5th test; in other words, you can't do any worse than a $78.82$ even if you don't take the 5th test. And the best you can do is $90.82$ if the most you can make on the test is $100$.

MPW
  • 43,638