The ratio of 16 to g is equal to the ratio of g to 49.
sandy wrote:
The ratio of 16 to g is equal to the ratio of g to 49.
Quantity A |
Quantity B |
g |
\(28\) |
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.
GIVEN: The ratio of 16 to g is equal to the ratio of g to 49.In other words, 16/g = g/49
Cross multiply to get: g² = (16)(49)
[Let's not find this product yet. You'll see why shortly]Notice that 16 = 4² and 49 = 7²
So, we get: g² = (4²)(7²)
We have a nice rule that says
(a^x)(b^x) = (ab)^xSo we can write: g² = 28²
IMPORTANT: Many people will conclude (incorrectly) that g must equal 28
However, we should also note that (-28)² = 28², so g could also equal -28
If g = 28, then Quantity A EQUALS Quantity B
If g = -28, then Quantity B is GREATER THAN Quantity B
Answer: D
Cheers,
Brent