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 result:

p =  97.2 %

Solution:

$$\begin{gathered} {e}_1=150\cdot {\displaystyle \frac{88}{100}}=132 \\ {e}_2=150\cdot {\displaystyle \frac{94}{100}}=141 \\ {e}_3=150\cdot {\displaystyle \frac{90}{100}}=135 \\ {\displaystyle \frac{p}{100}}\cdot 250+e_1+e_2+e_3={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250) \\ b={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250)-e_1-e_2-e_3={\displaystyle \frac{93}{100}}\cdot (3\cdot 150+250)-132-141-135=243 \\ p=100\cdot {\displaystyle \frac{b}{250}}=100\cdot {\displaystyle \frac{243}{250}}={\displaystyle \frac{486}{5}}={\displaystyle \frac{486}{5}}\mathrm{\%}=97.2\mathrm{\%} \end{gathered}$$

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