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?

Result

p =  97.2 %

Solution:

 e1=150⋅ 88100=132 e2=150⋅ 94100=141 e3=150⋅ 90100=135  p100⋅ 250+e1+e2+e3=93100⋅ (3⋅ 150+250)  b=93100⋅ (3⋅ 150+250)−e1−e2−e3=93100⋅ (3⋅ 150+250)−132−141−135=243  p=100⋅ b250=100⋅ 243250=4865=97.2=97.2% \ \\ e_{ 1 } = 150 \cdot \ \dfrac{ 88 }{ 100 } = 132 \ \\ e_{ 2 } = 150 \cdot \ \dfrac{ 94 }{ 100 } = 141 \ \\ e_{ 3 } = 150 \cdot \ \dfrac{ 90 }{ 100 } = 135 \ \\ \ \\ \dfrac{ p }{ 100 } \cdot \ 250+e_{ 1 }+e_{ 2 }+e_{ 3 } = \dfrac{ 93 }{ 100 } \cdot \ (3 \cdot \ 150+250) \ \\ \ \\ b = \dfrac{ 93 }{ 100 } \cdot \ (3 \cdot \ 150+250) - e_{ 1 } -e_{ 2 } - e_{ 3 } = \dfrac{ 93 }{ 100 } \cdot \ (3 \cdot \ 150+250) - 132 -141 - 135 = 243 \ \\ \ \\ p = 100 \cdot \ \dfrac{ b }{ 250 } = 100 \cdot \ \dfrac{ 243 }{ 250 } = \dfrac{ 486 }{ 5 } = 97.2 = 97.2 \%

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