The ratio of blue marbles to white marbles in a bag is 4 to 5 at this rate how many blue marbles are there if there are 15 white marbles

Sum up 4 and 5; result of that is 9.  Then 4/9 of the marbles in the bag are blue and 5/9 are white.

One of the easier ways in which you could solve this problem would be to write and solve an equation of ratios:

blue        4          x
= =
white       5        15

5x = 60, and thus x = 12.  There are 12 blue marbles.

Note that 12/15= 4/5 or 4:5.