Q1:
Note that C is defined by the question as the total cost of the bagel and coffee, not the cup of coffee itself. Thus, the equation B=2C-30 is wrong: what you should do is denote the coffee as a different variable X, so that B=2x-30, and C(total cost) = B+X = 2x-30+x = 3x-30.
Here comes the confusing part - we want B, not X. Isolate X from the first equation, and plug that into C:
If B=2x-30, then
2x=B+30
X=(B+30) /2
So if C=B+X, then C=(B+30)/2 + B = B+30+2B/2 which is indeed answer choice E.
I agree that this is confusing - I myself am partial to the plugging in approach. But even there you need to be careful not to turn C into "coffee": C is the total price of the bagel and coffee together. If Coffee is 50 cents, then bagel is 30 cents less than twice 50, or 70 cents, and C=Total cost = 70+50 = 120.
Plug in C=120 into the answer choices and eliminate those answer choices which do not equal the price of the bagel=70 cents:
2C+30 = 2*120+30 / 3 = 270/3 = 90 not equal to 70, so we eliminate.
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3
2C-30 = 2*120-30 / 2 = 210/2 = 105 - not equal to 70, so we eliminate
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2
C-10 = 120-10 / 3 = 110/3 - this is too small to be 70. Eliminate
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3
2C-10 = 2*120-10 / 3 = 240-10 / 3 = 230/3 - this is going to be a fraction, and not equal to 70. Eliminate.
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3
2C-30 = 2*120 - 30/3 = 240-30 / 3 - 210/3 = 70.
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3
Since this answer choice is the only one that matches your goal of 70 cents for C=120, it must be the right answer choice, and you needn't worry about the algebra.
