Problem of the Day


Consider the set \{x^2+x,9,10x,x^2-16x\}. If the arithmetic mean of this set is 3, which of the following could be the value of x?

A. \frac{1}{2}
B. 1
C. \frac{3}{2}
D. 3
E. 4

Reveal Answer

Answer

D. 3

See the Solution

Solution

[latexpage]

${x^2+x,9,10x,x^2-16x}$  has 4 terms. If the arithmetic mean of this set is 3, then the sum of the terms must be 12. This gives us the following equation:

$x^2+x+9+10x+x^2-16x=12$

$2x^2-5x-3=0$

$(2x+1)(x-3)=0$

$x=3,-\frac{1}{2}$

 


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