An author is having a book signing at a store. she agrees to give 30% of the profit to literacy programs and 25% of the profit to her manager. if the profit is $750.00, how much profit does she take home

This is just solving percentages which is fairly easy! :) 
To solve an equation like this, make all the percentages into decimals: 

-.30
-.25

Now, take 750$ and multiply it by .30 = 225$ 
Do the same with .25 % = 187.50

Now add the two variables together, and subtract from 750 $

The author will take home = 337.5