<p>If a, b, and c are numbers such that a over b = 3 and b over c = 7, then (a+b) over (b+c) is equal to which of the following?</p>
<p>Now, using basic plug-in strategies this problem is a cakewalk, so why doesn't the CB just tell us that yeah, making up values works best for this problem? Instead, they give us this horrendously obtuse 'explanation': </p>
<p>From a over b = 3 is implied that (a+b) over b = 4 (1)</p>
<p>And from b over c = 7 is implied that b over (b+c) = 7 over 8 (2)</p>
<p>If we multiply (1) and (2) together, we have that (a+b) over (b+c) = 4 times (7 over 8) = 7 over 2 ( b is canceled out).</p>
<p>Are people actually supposed to figure the problems like this? Who in a million years would think to set up and solve the problem like is shown in the explanation?</p>
<p>We should have a question of the day thread</p>
<p>I plugged in numbers. </p>
<p>a=3 b=1</p>
<p>b=1 c=1/7</p>
<p>so you get 4/(8/7)</p>
<p>so you get (7x4)/8</p>
<p>so you get</p>
<p>7/2</p>
<p>I do not understand why the CB would recommend any other way.</p>
<p>Nice job, plugging-in is way better
10Char</p>
<p>This is how I did it…:
7c = a/3 = b</p>
<p>Substitution gives you: a+b/a+c = 4b/(b + 1/7b)</p>
<p>^And that simplifies down to 3.5, which equals 7/2</p>
<p>Its faster if you just plug in numbers like a n00b.</p>
<p>Here is how I did it. I think doing it algebraically helps with fundamentals. Meaning you can tackle more problems when plugging in wont work. It also takes a little bit longer than plugging in but worth it.</p>
<p>a/b = 3 & b/c = 7 </p>
<p>now b = 7c. Plug that back in for b in a/b = 3.</p>
<p>a/7c = 3
a = 21c</p>
<p>now we have
a = 21c
b = 7c
and c </p>
<p>just subsitute the values
a+b/b+c </p>
<p>21c + 7c/ 7c + c </p>
<p>= 28c/8c</p>
<p>which = 7/2 cause the c’s cancel out.</p>
<p>simple and effective. takes no more than 20-30 seconds.</p>
<p>FYI: I got an 800 and almost made USAMO… and I just plugged in.</p>
<p>FYI: I did not get an 800 and did not participate in the USAMO… and I just plugged in.</p>
<p>FYI: I discovered general relativity and just plugged in.</p>