Inequality Word Problem Help Me Please

Question

Use the following breakdown to compute a student's grade:
$20\%$ for the midterm
$55\%$ for the test average
$25\%$ for the final exam

The student wants at least a B for the course. This means she needs a course grade of greater than or equal to an $80$. She earned an $84$ on the midterm and a $75$ for the test average. What does she need on the final exam to get at least a B for the course?

$$80 \leq \frac{84 + 75 + x.25}{3}?$$

Must write inequality, solve the inequality and answer with a sentence.

Answer 1

Assume that the student's grade includes $100$ scores:

• The score for the midterm (called $x$) is counted $20$ times

• The score for the test average (called $y$) is counted $55$ times

• The score for the final exam (called $z$) is counted $25$ times

Then the overall average of the student is $\frac{20x+55y+25z}{100}$.

For this specific problem, we need to solve $\frac{84\times 20+ 75\times 55+ 25z}{100}\ge 80$.

Then we should have $5805+25z\ge 8000 \Rightarrow25z\ge8000-5805=2195\Rightarrow z\ge87.8$

You can make the conclusion from here.

Answer 2

They got $84\%$ of $20$ points for the midterm and $75\%$ of $55$ points for the test average. How many more points are needed? What fraction of $25$ is that?