I need help with a math problem, I got the answer, but I need help understanding the steps, help?

Question

I will present the problem, and I will show my steps. I somehow figured out the answer, but I feel like there's something in between that I went wrong or should have done. Can someone please help me?

Here's the problem:

The cateferia sells each apple at one price and each banana at another price. For 1 apple and 2 bananas Jose pays $2.05. For 4 apples and 2 bananas Aprili pays $2.70. Maria buys 2 apples and 2 bananas. How much does she have to pay?

I started out letting X = how much Maria has to pay. So X = 2A + 2B.

I need to figure out what A & B is. So i did this:

(A+3B)/2.05 = (4A+2B)/2.70

--> it became 2.70(A=3B0=2.05(4A+2B)

--> then I came out to 4.0B = 5.5A

4.0B=5.5A ... I don't know where to go from there! but I noticed that the Answer is B = .55 and A = .40

Weird huh? I can't figure out how to get from that step to the answer.. maybe I'm missing a step or if someone can help me figure out why??

Answer 1

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