Question 1066909
 Vivienne made cupcakes to share with her friends and teachers at school.
 She gives half of her cupcakes to her friends. 
 Then, she gives 2 cupcakes to her teacher. 
 Finally, she gives 25% of the remaining cupcakes to her principal.
 She now has 12 cupcakes left. How many cupcakes did she bring to school?
:
let x = original number of cupcakes
:
x = .5x + 2 + .25(x - (.5x+2)) + 12
x = .5x + 2 + .25(x - .5x - 2) + 12
x = .5x + 2 + .25(.5x - 2) + 12
x = .5x + 2 + .125x - .5 + 12
x = .5x + .125x + 2 - .5 + 12
x = .625x + 13.5
x - .625x = 13.25
.375x = 13.25
x  = 36 cupcakes she brought to school