When 18 boys joined a group of why students, the ratio of boys to girls in the group became 4 : 5. write an algebraic expression for the number of girls in terms of y.

18 /(y + 18) = 4/9 <<<< answer. 
be careful the number of boys is in a ratio of the number of boys to the total.
Just to make sure I'm right, I solve it.
18 * 9 = 4*(y + 18)
162 = 4y + 72 Subtract  72 from both sides.
 90 = 4y Divide by 4
22.5 = y Never mind the 0.5. Does it work

18/22.5 = 0.8 
0.8 is the same thing as 4/5 
The problem makes no sense in the real world, but it does work out mathematically.

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°