You have 100 marbles. Half are blue, so fifty marbles are blue. Half of those 50 marbles are dark blue, so 50÷2 is 25. 25 is 1/4 of 100, which is also 25%.
What you do on one side of the equation, you do to the other. She added 10x on the right side and subtracted 10x on the left when she should have added 10x on both sides.