SOLUTION: Loretta picks apples for her grandfather to make apple cider. She brings him her cart with 420 apples. Her grandfather smile at her and says, "Thank you Loretta. That is 35% of t

Question 854218: Loretta picks apples for her grandfather to make apple cider. She brings him her cart with 420 apples. Her grandfather smile at her and says, "Thank you Loretta. That is 35% of the apples that we need." Use mental math to find how may apples Loretta's grandfather needs. Describe your method.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Doing this yourself, maybe with values other than I might use, would be much, much, much better than blindly using what I show here.

420 apples being only 35% of what the grandfather needs, if n is how much apples "needed", then this makes a proportion:

More conveniently used as

-
You want to apply some factor, approximately , to the 420, in order to estimate a better quantity of needed apples. what easy and near factor is this? You might have a feeling that is about 3. Maybe do IN YOUR HEAD.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The apples she brings and the apples she needs
are divided 35% - 65%,
Dividing each % by 5, I get 7 and 13, so the
fractions are:
7/20 and 13/20
If 420 apples is 7/20, then
60 apples is 1/20
and
13 x 60 = 780 apples is 13/20
So, her grandfather needs 780 apples
check:
780 / ( 780 + 420 ) = 780/1200
78/120 = 65%
OK

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