Darius saved 1/4 of his paycheck and spent 1/2 of the remaining money. He was then left with $12. What was the original value of Darius's paycheck?
start with x
saved 1/4 of x leaving him with (3/4)x
spent 1/2 of that , leaving him with (1/2)(3/4)x = (3/8)x
this is equal to 12
(3/8)x = 12
3x = 96
x = 32
check:
saved 1/4 of 32 , which is 8 , leaving him with 24
spent half of that, which is 12, leaving him with 12.
He had $ 32 at the start