Jenny spent 1 - 3/7 = 4/7 of her money.
Since 4/7 is equal to $24, then 1/7 is equal to $24/4 = $6.
So, Jenny originally had $6 x 7 = $<<6*7=42>>42.
Therefore, half of her original amount of money is $42/2 = $<<42/2=21>>21.
#### 21