Isabella is hoping to get an A on her college algebra course. With just the final exam left to take, she currently has an average of 92 on her exercises. The quizzes count for 40%, exercises count for30% of the class grade. What is the minimal grade that Isabella must have on the final exam to obtain an A in the class (90% or higher)
What is her quiz average? zero? 100?
I REALLY DON'T KNOW
To determine the minimal grade Isabella needs to get on the final exam, we can set up an equation using weighted averages.
Let's break down the weight distribution:
- Quizzes: 40%
- Exercises: 30%
- Final Exam: 100% - (40% + 30%) = 30%
To calculate the overall average, we need to consider the current average and the weight distribution. We'll represent the minimal grade on the final exam as 'x':
(0.4 * Average Quiz Grade) + (0.3 * Average Exercise Grade) + (0.3 * x) = Final Grade
Isabella currently has an average of 92 on her exercises, and we'll assume she performed consistently, so we can substitute this value into the equation:
(0.4 * Average Quiz Grade) + (0.3 * 92) + (0.3 * x) = Final Grade
To achieve an A (90% or higher) for the Final Grade, we can set up the inequality:
Final Grade ≥ 90
Substituting the equation for the Final Grade, we have:
(0.4 * Average Quiz Grade) + (0.3 * 92) + (0.3 * x) ≥ 90
Now we can solve for 'x', which represents the minimal grade Isabella needs to get on the final exam:
0.4 * Average Quiz Grade + 27.6 + 0.3 * x ≥ 90
0.4 * Average Quiz Grade + 0.3 * x ≥ 90 - 27.6
0.4 * Average Quiz Grade + 0.3 * x ≥ 62.4
0.3 * x ≥ 62.4 - 0.4 * Average Quiz Grade
x ≥ (62.4 - 0.4 * Average Quiz Grade) / 0.3
Therefore, Isabella needs to get a grade on the final exam that is equal to or higher than (62.4 - 0.4 * Average Quiz Grade) / 0.3 in order to obtain an A in the class.