<p>Can anyone please explain this question of the day answer to me, I don't understand the explanation given or anything.
The</a> Official SAT Question of the Day
I always see this type of question on the SAT and don't know how to solve it. Thank you</p>
<p>a / b = 3
a = 3b</p>
<p>b / c = 7
b = 7c</p>
<p>a + b = 3b + 7c
b + c = 7c + c = 8c</p>
<p>(a + b) / (b + c) = (3b + 7c) / (8c) = (21c + 7c) / (8c) = (28c) / (8c) = 28 / 8 = 14 / 4 = 7 / 2</p>
<p>The key to solving this problem is to simplify, eventually, every variable in the equation into a single variable, which in this case was c. That is the only way to break it down to a numerical answer.</p>
<p>You could also do it this way:
a/b = 3
a = 3b</p>
<p>b/c = 7
c = b/7</p>
<p>(a+b)/(b+c) = (3b + b)/(b + b/7) = 4b/(8b/7) = 28/8 = 7/2</p>
<p>I found this way to be a bit quicker. However, crazybandit’s way of doing the problem is absolutely correct.</p>
<p>Thank you! That made a lot more sense than their explanation, I didn’t realize that you had to substitute twice.</p>