<p>SAT question of the day for Jan. 3, 2010. I eventually got the right answer after my second go at it, but I wanted a more solid procedure---Collegeboard's explanation made no sense to me...could someone explain it to me in their own words?</p>
<p>If a, b, and c are numbers such that a over b eq 3 and b over c eq 7, then a plus b over b plus c is equal to which of the following?</p>
<p>A. 7 over 2
B. 7 over 8
C. 3 over 7
D. 1 over 7
E. 21</p>
<p>The answer is A.</p>
<p>I just plugged in numbers.
Let’s suppose
a=21
b=7
c=1
21/7=3
7/1=7</p>
<p>so…
(21+7)/(7+1)=28/8=7/2
I try to avoid all that algebra mumbo jumbo…</p>
<p>I did the exact same thing, but I want to understand Collegeboard’s method.</p>
<p>Yeah I did it that way too. College Board always has to complicate things. I’ll try and explain it.</p>
<p>a/b=3, and b/b=1
so a/b+b/b=(a+b)/b=4. That’s equation 1</p>
<p>b/c=7, so c/b=1/7, and b/b=1
so c/b+b/b=(c+b)/b=8/7
so b/(b+c)=7/8. That’s equation 2. Multiply them together</p>
<p>(a+b)/b * b/(b+c) = (a+b)/(b+c)=4*(7/8)=7/2</p>
<p>Hope that helps</p>
<p>I did it with a=42, b = 14, and c = 2, and got the right answer.
Does it matter which numbers you plug in? Any max/min limits?</p>
<p>i did:
a=3b, b=7c, then plug it in to have 4b/8c. Reduce it: b/2c. since b/c is 7, then
(1/2)(b/c)=(1/2)(7)=7/2 and A is the answer.</p>
<p>Interesting how everyone has their own way to look at it. I started out like jerry, then put everything in terms of c : a=3b, b=7c, so a=21c. Then a+b is 28c and b+c is 8c, so 28c/8c reduces to 7/2.</p>
<p>Thanks Secret Asian Man, I think I get it now, but I don’t understand why you multiply for the last step. </p>
<p>@ncm2012, the numbers that you plug in shouldn’t matter as long as they satisfy both of the equations.</p>
<p>I think you might wanna use Collegeboard’s method for more complicated problems.</p>
<p>I think that you multiply at the end because (a+b)/b times b/(b+c), and b cancels out. This means that (a+b)/(b+c) is equal to (a+b)/b times b/(b+c), and we know that (a+b)/b=4. Because the equations are equal, you can multiply (a+b)/b (4) times b/(b+c) (7/8). I hope this makes sense. Would this problem be considered easy or hard on the SAT?</p>