## Discussion

If a = 3b, b2 = 2c, 9c = d, then (A) 1/2 (B) ... (C) ... (D) ... (E) ... (F) ...
*This question is included in Nova Math - Diagnostic: Test / Review, question #2

The solution is

Posted: 12/30/2011 07:42
I am in 7th grade and I am about to take the SAT and want to be prepared. While looking at this I had trouble solving and have not seen stuff like this before. With this in mind the work afterwards did not help me under stand it better. Thank you for you assistance.
Posted: 12/30/2011 09:33
This is substitution, while common substitution gives you things like x=5 or n=8 for you to work with, a similar thing is happening right here, however now they give you x=2y, y=4z and z=2.
Substituting y=4(2) so y=8, x=2(8) so x=16.

Given is:
a = 3b
b^2=2c
9c=d

And we start out with:
a^2 / d
plug in 9c for d
(a^2) / (9c)
plug in 3b for a
((3b)^2) / (9c)
now we simply the numerator (3b)^2 becomes 9b^2
Now we have (9)b^2 / (9)c
Divide both numerator and denominator by 9
(1)b^2 / (1)c ergo b^2 / c
Now we plug 2c for b^2 as given and we'll get
2c / c ergo 2c / 1c
Now divide both numerator and denominator by c
2 / 1 = 2 and that's our answer.

Niels

Greetings from Holland
Posted: 01/16/2012 15:49
How did they get 2c/c?
Posted: 01/16/2012 19:25
(1)b^2 / (1)c ergo b^2 / c
Now we plug 2c for b^2 as given and we'll get
2c / c ergo 2c / 1c

The question includes equations, one of them is b^2 = 2c which in turn means everywhere we end up with b^2 in our working equation we can replace it with 2c. We can also replace 2c for b^2 if that's more convenient since their equal.
Assuming you got the part where we end up with:
b^2 / c
All we do in the next step is the replacement from b^2 to 2c:
2c / c

Niels
Posted: 02/26/2012 18:08
Why Dose the c come to top
Posted: 05/23/2012 23:30
Can you explain the problem again because aren't you suppose you suppose to put (9c)^2 since its a^2 / b^2?
Posted: 05/24/2012 06:55
Please show your step(s) that take you to a^2 / b^2
Posted: 05/24/2012 07:14
a^2 / d >> sub. a for 3b
(3b)^2 / d >> sub. d for 9c
(3b)^2 / 9c >> simplify numerator
(9)b^2 / 9c >> divide numerator and denominator by 9
(1)b^2 / (1)c or just b^2 / c
b^2 / c >> sub. b^2 for 2c
2c / c >> divide num. and den. by c
2(1) / (1) or just 2 / 1
2 / 1 = 2

Niels
Posted: 10/11/2012 01:06
so for this problem a can be either 3b or b^2 and b^2 can be either 2c or 9c? i've never sloved this problem..
Posted: 12/04/2012 15:46
The answer is (B).
Posted: 07/29/2013 16:31
if a=3b,b^2=2c,9c=d then a^2/d= ????? 