If xy=4, x/y=36, for positive numbers x and y, y=?
A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6
*Answer will be posted in 2 days.
If xy=4, x/y=36, for positive numbers x and y, y=?
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- Max@Math Revolution
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Given: (1) xy = 4; and (2) x/y = 36Max@Math Revolution wrote:If xy=4, x/y=36, for positive numbers x and y, y=?
A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6
*Answer will be posted in 2 days.
From (2), solve for x by multiplying both sides of the equation by y: x = 36y
Now substitute this into the first equation: (36y)y = 4
36y^2 = 4
y^2 = 1/9
y = +/- 1/3
But we're told from the prompt that y must be positive, so +1/3 is the only possible solution. Answer choice: C
800 or bust!
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Another alternate is to check the answer choices.Max@Math Revolution wrote:If xy=4, x/y=36, for positive numbers x and y, y=?
A. 1/2
B. 2
C. 1/3
D. 3
E. 1/6
A) y = 1/2
Since xy = 4, we can conclude that x = 8
If y = 1/2 and x = 8, then x/y = (8)/(1/2) = 16.
NOT GOOD, x/y is SUPPOSED to equal 36
ELIMINATE A
B) y = 2
Since xy = 4, we can conclude that x = 2
If y = 2 and x = 2, then x/y = 2/2 = 1.
NOT GOOD, x/y is SUPPOSED to equal 36
ELIMINATE B
C) y = 1/3
Since xy = 4, we can conclude that x = 12
If y = 1/3 and x = 12, then x/y = (12)/(1/3) = 36.
GREAT! x/y is SUPPOSED to equal 36
Answer: C
- Max@Math Revolution
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If we substitute in x=4/y, from 4/y^2 =36, we get y^2=1/9. Hence, y=1/3. Thus, the correct answer is C.
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