SAT Q: If 3a-c=4b and 3a+4b-c=12 , what is the value of b?

[gusterguy]

OK, this is from a practice take at home SAT test I'm working on...I think it's an Algebra II problem.

If 3a-c=4b and 3a+4b-c=12 , what is the value of b?

They give 5 answer choices and one is "it cannot be determined from the information given" - I want to believe it's that one but they usually never are.

I tried to start by putting the equations in the same format but in the first one, if I brought the 4b over to the other side it would leave nothing. I solved for b in the first equation and then plugged it into the second equation, but that wasn't helpful as I still had two variables.

Any help to at least lead me in the right direction?

Thank you!
Jeff

 

[soroban]

Re: I cannot for the life of me figure this out

Hello, Jeff!

If .\(\displaystyle 3a-c\:=\:4b\) .and .\(\displaystyle 3a+4b-c\:=\:12\), what is the value of \(\displaystyle b\) ?

\(\displaystyle \text{We have: } \;\begin{array}{cccc} 3a -4b- c &=& 0 & [1]\\ 3a + 4b - c &=& 12 & [2] \end{array}\)

\(\displaystyle \text{Subtract [1] from [2]: }\;8b \:=\:12\quad\Rightarrow\quad \boxed{b \:=\:\frac{3}{2}}\)

 

[andpwn]

from first equation: b= (3a-c)/4 from second equation b = (12 - 3a +c)/4
now just plug in b from first eq. to the second and you'll get b = 3

 

[galactus]

b is not 3. It is indeed 3/2.

By substitution:

Solve the first for c:

c=3a-4b

Sub into the other equation:

3a+4b-(3a-4b)=12

8b=12

b=3/2

 

[andpwn]

oops my mistake :?