The roots of the word percent translate roughly to "for each 100." If we have 3% of something, it's equivalent to saying we have 3/100 of that thing. What this means is that finding a percent of something is the same thing as finding a fraction of that thing, and then changing its denominator to 100.
Here, we'll find the fraction of blue marbles in the bag first. If red marbles take up 17/20 of the total marbles, we know that the remaining 3/20 must be blue. To find out what percentage that corresponds to, we'll need to convert 3/20 into an equivalent factor with a denominator of 100. We don't know what will be in the numerator yet, so we'll call that x:
[tex] \frac{3}{20}= \frac{x}{100} [/tex]
To find x (our percentage), we can simply multiply both sides of our equation by 100 to get
[tex] \frac{3\cdot100}{20}=x\\\\
3\cdot5=x\\
15=x [/tex]
So, the blue marbles take up 15% of the total number of marbles.
