Question

# Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. To earn an A in a course, you must

Modeling
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. To earn an A in a course, you must have a final average of at least 90%. On the first four examinations, you have grades of 86%, 88%, 92%, and 84%. If the final examination counts as two grades, what must you get on the final to earn an A in the course?

2021-07-03
Let's note: x=the grade to be taken on the final examination
We write the inequality modeling the problem: $$\displaystyle\frac{{{0.86}+{0.88}+{0.92}+{0.84}+{2}{x}}}{{6}}\Rightarrow{0.90}$$
We solve the inequality: $$\displaystyle\frac{{{3.5}+{2}{x}}}{{6}}\Rightarrow{0.90}$$
$$\displaystyle{3.5}+{2}{x}\Rightarrow{6}{\left({0.90}\right)}$$
$$\displaystyle{3.5}+{2}{x}\Rightarrow{5.4}$$
$$\displaystyle{3.5}+{2}{x}-{3.5}\Rightarrow{5.4}-{3.5}$$
$$\displaystyle{2}{x}\Rightarrow{1.9}$$
$$\displaystyle{x}\Rightarrow\frac{{1.9}}{{2}}$$
$$\displaystyle{x}\Rightarrow{0.95}$$