Mackenzie's question is missing a key word, and Nathan B's query is putting his finger right on the missing element: Are there 50 more quarters than dimes, or 50 fewer quarters than dimes? Obviously these two conditions will not give the same answers.
But we can deduce...

Here's an easier way to do it:
The percentages of the two alloys we're mixing are 16 and 20. The percentage we want to get to is 19. That differs from 16 by 3, and from 20 by 1. Since the percentage we want is 3 times as far from the 16% value as it is from the 20%...

Here's an easier way to do it:
The prices per pound of the two types of coffee we're mixing are $20 and $80. The price point we want to get to is $40. That differs from the $20 price by $20, and from the $80 price by $40. Since the desired price point is twice as far from the $80 price...

Here's an easier way to do it:
The prices per pound of the two types of coffee we're mixing are $20 and $80. The price point we want to get to is $40. That differs from the $20 price by $20, and from the $80 price by $40. Since the desired price point is twice as...

This problem can also be done without resorting to complex numbers.
Complete the square on the denominator:
s2 + 2s + 5 = (s+1)2 + 4
Since the denominator is now expressed in terms of s+1, express the numerator...

Both of the previous answers give the result as 4%. However, that's the percentage of the cake
that has been eaten. The question asks what percentage of the cake
is left, which is the remaining 96%.

Sorry, but this answer is wrong. The exponent (cx+d) applies only to the b; the a is not part of the base. So taking the base (ab) logarithm is the wrong move. George C's answer, complicated as it is, is correct.

1000/2 is one very easy way. But the real answer is, get a new calculator! You can get a simple calculator as cheap as a buck (at a Dollar Tree or someplace similar). Why waste your time fooling around with one with broken keys?

I don't see any reason to do this in decimal form. Like many fraction problems, it's done most easily as a common fraction.
Begin by putting the .21 over the .33. Now you have .21/.33. Get rid of the decimals by multiplying by 100/100. that gives you 21/33. ...

This is a partial fractions problem. But notice that it's an improper fraction (because the highest power in the numerator is as large as the highest power in the denominator), so before you can apply the partial fractions technique, you need to use long polynomial division to break...

The number 8 is the correct number, and so is the process you described for how you got it. However, what the 8 represents is not f(x)dx, but what you stated in your question, namely, the definite integral from 1 to 2 of (4x3 - 3x2). So if you answered the question by saying "f(x)dx...