Answer:
The fraction of the original amount of paint is available to use on the third day is [tex]\frac{4}{9}[/tex]
Solution:
Given Data.
Day 1 = [tex]\frac{1}{3}[/tex] paint
Day 2 = [tex]\frac{1}{3}[/tex] of remaining paint .i.e [tex]1 - \frac{1}{3} = \frac{2}{3}[/tex]
We can find the original amount of paint is available to use on the third day can be found using the below steps.
After the first day, there is [tex]1 - (\frac{1}{3} \times 1)[/tex] gallons left
After the second day, there is a total of [tex]\frac{2}{3} - (\frac{1}{3} \times \frac{2}{3})[/tex]
Evaluate the above expression:
= [tex]\frac{2}{3} - \frac{2}{9}[/tex]
= [tex]\frac{4}{9}[/tex]
After the second day, there is a total of [tex]\frac{4}{9}[/tex] gallons left.
Therefore, the fraction of the original amount of paint that is left is [tex]\frac{4}{9}[/tex]
