Jack's mother asked him to buy 2 * 4 = <<2*4=8>>8 bottles of water.
Thus Jack bought 4 + 8 = <<4+8=12>>12 bottles of water in total.
Altogether, the bottles of water cost 12 * $2 = $<<12*2=24>>24.
The cheese cost 1/2 * $10 = $<<10*0.5=5>>5.
So Jack spent $24 + $5 = $<<24+5=29>>29 on water and cheese.
Since he started with $100, he now has $100 - $29 = $<<100-29=71>>71 left.
#### 71