Geography tests

On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?

Correct answer:

p =  97.2 %

Step-by-step explanation:

$$\begin{gathered} e_1=150\cdot \frac{88}{100}=\frac{150\cdot 88}{100}=\frac{13200}{100}=132 \\ {e}_2=150\cdot \frac{94}{100}=\frac{150\cdot 94}{100}=\frac{14100}{100}=141 \\ {e}_3=150\cdot \frac{90}{100}=\frac{150\cdot 90}{100}=\frac{13500}{100}=135 \\ \frac{p}{100}\cdot 250+e_1+e_2+e_3=\frac{93}{100}\cdot (3\cdot 150+250) \\ b=\frac{93}{100}\cdot (3\cdot 150+250)-e_1-e_2-e_3=\frac{93}{100}\cdot (3\cdot 150+250)-132-141-135=243 \\ p=100\cdot \frac{b}{250}=100\cdot \frac{243}{250}=\frac{100\cdot 243}{250}=\frac{24300}{250}=\frac{486}{5}\%=97.2\% \end{gathered}$$

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