Step-by-step explanation:
1. She tried 16 cups of fruit juice and 4 cups of ginger ale. That was too fruity.
Here the taste was too fruity, and the ratio used is 16:4, so in the next attempt, she needs to use less than 16 cups of fruit juice and or more than 4 cups of ginger ale.
Here the quotient between the cups of juice and ginger is: 16/4 = 4
2. She tried 10 cups of fruit juice and 8 cups of ginger ale. That was too gingery.
Now, the ratio is too gingery, so she needs to use more fruit juice and less ginger.
Here the quotient between the cups of juice and ginger is: 10/8 = 1.25
so at this point, we know that if the quotient is 1.25 or less the mixture is too gingery, and if it is 4 or more is too fruity, so the range we need to point is (1.25, 4)
3. She tried 10 cups of fruit juice and 1 cup of ginger ale. That was too fruity.
Now the ratio is 10:1, she only diminished the amount of ginger used, now she needs to increment the number of cups of ginger used, but she needs to be careful to not use more than 7. (because she already knows that the ratio 10:8 ends being too gingery).
Here the quotient between the cups of juice and ginger is: 10/1 = 10, the range of interest still is: (1.25, 4)
4. She tried 8 cups of fruit juice and 4 cups of ginger ale. That was a little too gingery.
now the ratio is 8:4, and the mix ends being a little gingery.
This means that she may need to use a little bit less ginger or a little bit more juice.
Here the quotient between the cups of juice and ginger is: 8/4 = 2
So now the range of interest is (2, 4)
5: Now, knowing that the ratio 8:4 was a little bit gingery, it is a good idea to use a cup lees of ginger and test the mixture. If the mixture is still a little bit gingery, you can add a cup of juice, in this case, the ratio will be 8:3
If when you remove the first cup of ginger, the mixture now is a little bit juicy, you can add again the cup of ginger and a cup of juice, making the ratio 9:4
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