Carcass wrote:
\(\frac{x^2+4}{5}=\frac{x+8}{3}\)
Quantity A |
Quantity B |
\( x\) |
\(x^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Given: \(\frac{x^2+4}{5}=\frac{x+8}{3}\)
Cross multiply: \((x^2+4)(3) = (5)(x+8)\)
Expand: \(3x^2 + 12 = 5x + 40\)
Subtract \(5x\) from both sides of the equation: \(3x^2 - 5x + 12 = 40\)
Subtract \(40\) from both sides of the equation: \(3x^2 - 5x - 28 = 0\)
Factor: \((3x + 7)(x - 4) = 0\)
So, EITHER \((3x + 7) = 0\) OR \((x - 4) = 0\)
If \((3x + 7) = 0\), then \(x = \frac{-7}{3}\), in which case \(x^2\) is some POSITIVE number
In this case,
Quantity B is greater.
If \((x -4) = 0\), then \(x = 4\), in which case \(x^2 = 16\)
In this case,
Quantity B is greater.
In BOTH possible cases,
Quantity B is greater, so the correct answer is B
Cheers,
Brent