Problem #1

Eleven students have a math test with the average score 65. The difference between the highest and the lowest scores is 20. If the highest and the lowest scores are ignored then average is 63. The highest score is …

Solusi
Nilai 11 siswa, misalkan x1, x2, …, x11. Reratanya 65.
\frac {x_{1} + x_{2} + ... + x_{11}}{11} = 65
atau
x_{1} + x_{2} + ... + x_{11} = 65 \times 11 = 715 (pers. i)

Misalkan x1 nilai tertinggi dan x11 nilai terendah, selisihnya 20.
x_{1} - x_{11} = 20 (pers. ii)

Rerata nilai tanpa menyertakan nilai tertinggi dan nilai terendah adalah 63.
\frac {x_{2} + x_{3} + ... + x_{10}}{9} = 63
atau
x_{2} + x_{3} + ... + x_{10} = 63 \times 9 = 567 (pers. iii)

Substitusi pers. iii ke pers. i
x_{1} + x_{2} + ... + x_{10} + x_{11} = 715
x_{1} + x_{11} + (x_{2} + ... + x_{10}) = 715
x_{1} + x_{11} + 567 = 715
x_{1} + x_{11} = 148 (pers. iv)

Berdasarkan pers. ii dan pers. iv
x_{1} + x_{11} = 148
x_{1} - x_{11} = 20

Eliminasi x_{11} , maka diperoleh:

2x_{1} = 168
x_{1} = 84

Jadi, nilai tertinggi = 84.
 

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