SOLUTION: john has taken three exams in math 11 this semester. His average grade is 84. The highest grade is 18 points more than the average of the two lower grades, and his lowest grade is

Algebra ->  Average -> SOLUTION: john has taken three exams in math 11 this semester. His average grade is 84. The highest grade is 18 points more than the average of the two lower grades, and his lowest grade is       Log On


   

Question 1117042: john has taken three exams in math 11 this semester. His average grade is 84. The highest grade is 18 points more than the average of the two lower grades, and his lowest grade is 15 points less than the average of the two higher grades. What scores did he get for the three exams?
Answer by josgarithmetic(39614) About Me  (Show Source):
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three exams in math 11 this semester. His average grade is 84. The highest grade is 18 points more than the average of the two lower grades, and his lowest grade is 15 points less than the average of the two higher grades. What scores did he get for the three exams?
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first second third, x, y, z

x%2By%2Bz=3%2A84
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%28x%2By%29%2F2%2B18=z
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%28y%2Bz%29%2F2-15=x

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system%28x%2By%2Bz=252%2Cx%2By-2z=-36%2Cy%2Bz-2x=30%29
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system to use: system%28x%2By%2Bz=252%2Cx%2By-2z=-36%2C2x-y-z=-30%29

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%28x%2By-2z%29%2B%282x-y-z%29=-66
3x-3z=-66
x-z=-22
or
z-x=22
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system%28%28x%2By%29%2Bz=252%2C%28x%2By%29-2z=-36%29
E1-E2eliminatesxandy
3z=288
highlight%28z=96%29--------highest score

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Returning to x-z=-22, and substituting for z,
x=z-22
x=96-22
highlight%28x=74%29--------expected to be lowest score
.
highlight%28y=82%29