<p>What is the fastest method to solving this problem? I don't think I even half-understand the solution given by the College Board...</p>
<ol>
<li>If x, y, and z are positive numbers and 2x=3y=4z, then the value of x+y+z is how many times the value of x?</li>
</ol>
<p>A) 13/6
B) 17/6
C) 13/2
D) 17/2
E) Cannot be determined</p>
<p>A is this correct… ?
</p>
<p>Exactly the explanation that i was going to type.</p>
<p>To solve this, one has to find y and z in terms of x. From 2x=3y=4z, we get y=2/3x and z=1/2x. So, x+2/3x+1/2x=13/6x. A is correct.</p>
<p>^ Wow… Thank you so much. I found the CB explanation to be un-necessary and long. I tried doing that but then I got x=3/2y, x=2z. I didn’t bother to find y, and z, in terms of x. So that’s why I got confused.</p>
<p>just plug in numbers.
Say x=6
Then 3y=12
y=4</p>
<p>4z=12
z=3
6+3+4=13
13/x (aka 6) =13/6</p>
<p>Make everything in terms of x.</p>
<p>
</p>
<p>That is the smart way. But recognize that using x=6 is not random. You want a number that works for 2x=3y=4z. Having 2x = 12 should be by design.</p>
<p>Also, it is always smart to look at the proposed solutions. They almost give it away, as x should be 2 or 6! </p>
<p>A) 13/6
B) 17/6
C) 13/2
D) 17/2</p>