Carcass wrote:
y>9z>2
Quantity A |
Quantity B |
x2yz−8x2z+3yz−24z |
0 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
This is a tricky question, but with some factoring we can make sense of it.
x2yz−8x2z+3yz−24zFirst, notice that
x2yz−8x2z has common factors of
x2 and
z, so lets factor those out.
x2z(y−8)+3yz−24zNow notice that
3yz−24z has common factors of
3 and
z, so let's factor those out:
x2z(y−8)+3z(y−8)From here, we can factor out a factor
(y−8):
(y−8)(x2z+3z)Then from here we can factor out a factor of
z from
(x2z+3z):
(y−8)(z)(x2+3)Since
y>9,
y−8>0, so the
(y−8) portion of that equation is positive.
Since
z>2, we know that the
(z) portion of that equation is positive.
Finally, since
x2 is always positive or 0, and
3 is positive,
(x2+3) is positive.
So we have a
positive*positive*positive in Quantity A, and 0 in Quantity B.
Therefore, Quantity A is greater.