Question

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

Answer 1

1/3 of remained 2/3 is 2/9. We’ve used 1/3+2/9 = 3/9+2/9 = 5/9. So we’ve used 5/9 and we have 4/9 of the paint

Answer 2

The fraction of the original amount of paint is available to use on the third day is
`(4)/(9)`

Solution:

Given Data.

Day 1 =
`(1)/(3)` paint

Day 2 =
`(1)/(3)` of remaining paint .i.e
`1 - (1)/(3) = (2)/(3)`

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
`1 - ((1)/(3) * 1)` gallons left

After the second day, there is a total of
`(2)/(3) - ((1)/(3) * (2)/(3))`

Evaluate the above expression:

=
`(2)/(3) - (2)/(9)`

=
`(4)/(9)`

After the second day, there is a total of
`(4)/(9)` gallons left. Therefore, the fraction of the original amount of paint that is left is
`(4)/(9)`