Hi all. There’s something about this question that I cannot get out of my head.

I’ve watched Greg’s explanation several times and (spoilers), he comes to the conclusion that the answer is A – but in watching his explanation, I can’t help but think we’re approaching this question incorrectly. Here’s my reasoning – please help me see where I diverge from the correct course!

We have Alloys A and B. These alloys are made up of two basic elements. We’ll call these elements **e1** and **e2.** Alloy A is a ratio of 5e1 : 3e2. Alloy B is a ratio of 1e1 : 2e2. Now, we’re told that there’s a new Alloy X, which is made by mixing alloys A and B in a ratio of 4:3, and we’re asked to solve for the composition of the two basic elements (e1 and e2) in Alloy X.

So, I take 4 parts Alloy A and 3 parts Alloy 3 and add them together:

4(5e1 / 3e2) + 3(1e1 / 2e2)

I multiply out the 4 and the 3 (interpreting them as 4/1 and 3/1, respectively):

(20e1/3e2) + (3e1/2e2)

I multiply the left figure by 2/2 and the right by 3/3 to get the same base:

(40e1/6e2) + (9e1/6e2)

and then add:

49e1/6e2

Which leads me to believe that when we mix 4 parts Alloy A with 3 parts Alloy B, we get Alloy X, which is 49 parts e1 to 6 parts e2.

In the video explanation, I feel like we didn’t solve for the composition of the **basic elements.** Obviously, my took me to a non-existent answer choice, so I’m in the wrong here, but I’m having trouble seeing my error. Can anyone point out my mistake?

Thank you!