This question well explanned

 Alloys A and B are made up of two basic elements. In alloy A, the ratio of the elements is 7 : 5 and in alloy B it is 3 : 4. A new alloy is formed by mixing alloys A and B in a ratio of 5 : 4. What is the ratio of the basic elements in the new alloy? 

A) 389 : 367

B) 390 : 368

C) 391 : 369 

D) 392 : 370

E) 393 : 371

On these question how we gonna use the proportionalitites to sum, see that just sum 7 with 3 and multiply by 5, because the 7 parts of the metal is for a total of the first alloy and not for the second, so we gonna covert all the alloys to the same quantity, type if I was making alloy my mother explained to me is that way we had 10 cadinhos, and and never gonna got out of that is of the time og Jesus, so I can have 3 parts, but always 3 parts of 10, so I would never need convert is sacramentada, but in here the cadinhos are of diferernt numbers, I had a aunt that had a mine in Juazeiro, is the gold 8 quilates, is the gold mix with silver, she also sales gol from Portugal that was red with cooper in place of silver, so let's convert:

so is 7/12: 5/12 because we have 12 cadinhos for proportion of 7 to 5, so go got more one cadinho or kick if you have more than 7+5

The second is 3/7: 4/7 because I gonna have to have 3 cadinhos for a and more 4 cadinhos for b.

I fail here I mutliplpy the all the a for the same and is to mulyiply all the A for the same proportion, once my fahter said the problem of genius they simplfy and got mistaken.

My father so mad because I didn't want to know at the time what happens that wasn't right, he said that genius are preguiçosos that I need to investigate till discover, why the answer wasn't right, I was satisfied to discover the proportion and I wanted to the rest went to hell, I asked to my father solved to me.

So is the right answer:

the partial results of the league make with alloys of the metals 5:4

5x7/12 + 4x3/7    :    5x5/12 + 4x4/7

35/12 + 12/7        :    25/12 + 16/7

know reduzindo all the elements of the same side for the same base that is 84 and reduzindo to the same base all the same elements of the second proportions also is 84

To people know this = equal, this : prorpotion;

245+144/84    :    175+192/84

389/84            :    367/84            How this is a proportion see the bases are the same so I can simplify and cancel the bases and is the proportion had in common divisors I coul simplify:

389:367, today I saw the solution for it in a site but without justification just applied, so I like to explain for you why?

Rute Bezerra de Menezes Gondim