Petra has 49 blue marbles and two red marbles. How many marbles must Petra remove so that

90 % of her marbles are blue?

(A 10

(B) 15

(C) 20

(D) 30

(E) 31

I'm assuming Petra is only removing blue marbles, and she is keeping the 2 red marbles the whole time.

If so, then she starts with 49 blue marbles and ends up with 49-x blue marbles after removing x blue marbles. Overall she starts with 49+2 = 51 marbles total and ends up with 51-x marbles total after taking away x blue marbles.

(49-x) / (51-x) represents the proportion of blue marbles after we take those blue ones away. We want the proportion to be 0.90

(49-x) / (51-x) = 0.90

49-x = 0.90 (51-x)

49-x = 0.90 (51) + 0.90 (-x)

49-x = 45.9-0.90x

-x+0.90x = 45.9-49

-0.10x = - 3.1

x = - 3.1 / (-0.10)

x = 31

Petra must remove 31 blue marbles so that 90% of the marbles are blue. Answer: (E) 31