For the sake of showing work I will replace the empty space with an x like so...

To find out what x is you must cross multiply (aka butterfly)
***Image of this step is attached below
9*x = 10*90
9x = 900
Next divide 9 to both sides to finish isolating x. Since 9 is being multiplied by x, division (the opposite of multiplication) will cancel 9 out (in this case it will make 9 one) from the left side and bring it over to the right side.
9x ÷ 9 = 900 ÷ 9
1x = 100
x = 100
To make these fractions equivalent the empty spot must be 100

Hope this helped!
~Just a girl in love with Shawn Mendes
Mental way:
415 / 51.9 * 100 = 800 students in the school.
detailed way:
x is the amount of students in the school.
51.9% * x = 415
(divide both sides by 51.9% (or 0.519))
x = 800 students
Answer: $20
Explanation: If you have $17.70 after 2 games and $14.25 after 5, you do 17.70-14.25; which equals $3.45 so in 3 games you spend $3.45 now divide that by 3 to determine the unit value; which equals $1.15, so you spend $1.15 on every game now times that by 2 which is $2.30 and add that to $17.70 to see the original amount of money on the card which was $20