Amber needs to buy 35 gallons of paint to paint the interior of her house. she needs green, beige, and white in the ratio 3: 5: 2. how many gallons of white paint does she need?

The ratio of 3:5:2 mean 10 gallons of paint from what quantitie 2 gallons are wite
so total needs 35 gallons so this mean 3*10 +5 gallons 
from these 10 gallons 2 gallons are white so from 3*10 gallons will be 3*2 gallons white what is 6 gallons white 
but there are again 5 gallons till 35 gallons so than we know that from 10 gallons has 2 gallons white so from this result that from 5 gallons will be 1 gallon white 
so these above resulted 6 gallons white plus assumed with this 1 gallon white so total will be 6+1=7 gallons of white paints she need 

She needs seven gallons of white paint
3:5:2 total=10
_:_:_=35
10*3.5=35
3*3.5=10.5
5*3.5=17.5
2*3.5=7
10.5+17.5+7=35