Question

in one class, homework is worth 40% of the final grade, each of 3 projects is worth 10%, and a final exam is worth 30%.
(a) if a student has an 86 homework average and a 95 on the first project, what is the students grade at this point?
(b) if the same student from part (a) gets a 76 on the second project and a 78 on the third project, what is the lowest grade the student can get on the final exam to get an 80 overall in the course?

(a) the grade at this point is
(simplify your answer. round to the nearest tenth as needed.)

Explanation:

Step1: Calculate homework contribution

Homework: $86 \times 0.4 = 34.4$

Step2: Calculate first project contribution

First project: $95 \times 0.1 = 9.5$

Step3: Sum contributions for part (a)

Total: $34.4 + 9.5 = 43.9$

Step4: Calculate all project contributions for part (b)

Project avg: $\frac{95+76+78}{3} = 83$; Project total: $83 \times 0.3 = 24.9$

Step5: Set up equation for final exam

Let $x$ = final exam grade. Equation: $34.4 + 24.9 + 0.3x = 80$

Step6: Solve for $x$

$59.3 + 0.3x = 80$ → $0.3x = 20.7$ → $x = 69$

Answer:

(a) 43.9
(b) 69