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!
The problem with this that you are converting ratio to numbers, for instance you could also have
5e1, 3e2 for A but 2e1, 4e2 for B
This way you get (5+2)7e1 in total
and (3+4)7 e2 in total
e1:e2 = 7:7 = 1:1
Thanks for the response!
That’s a good point – I understand that Alloy B could be 1e1, 2e2… 2e1, 4e2… (X)e1, (2X)e2… Any of those would work.
… but what’s confusing me is that the question states that Alloy X must be made with a 4:3 ratio of Alloy A to Alloy B.
If I did…
Alloy A - 5e1, 3e2 (5:3 ratio)
Alloy B - 2e1, 4e2 (1:2 ratio)
Isn’t this 1x Alloy A and 2x Alloy B? This is a 1:2 ratio, not a 4:3 mix required by the question.
Ah my bad for 5e1, 3e2 for A but 2e1, 4e2 for B
The final mixture would be:
e1 = 20 + 6 = 26
e2 = 12 + 12 = 24
e1:e2 = 13:12
Which is different than what you get when B = 2e1 and 4e2
I was basically trying to demonstrate that the ratio alone of e1 and e2 cannot be used to solve in this manner
The confusion here is that the final Alloy X is in ratio 4:3 (or any multiplied form of it such as 8:6). This means that total parts of A must be 4, 8, 12, etc. The total parts of B must 3, 6, 9, etc.
What vidishas99 did in the first post is correct. Alloy X was multiplied by 2:2 (4:3 * 2:2 = 8:6).
The question stem already provides Alloy A in a total of 8 total parts (5+3=8).
Alloy B must be changed from 3 total parts to 6. We can multiply 1:2 by 2:2 to do this. This gives us 2:4 giving us 6 total parts (2 parts of e1 + 4 parts of e2 = 6 total parts).
Now we can add both parts of the alloy together since they are already in the correct mixing ratio as stated by the stem (4:3).
Add all of the E1 (5+2 = 7). Add all of the E2 (3+4 = 7).
E1:E2 = 7:7 = 1:1
