Rachel bought some nougats to share with her friends. She gave 8 nougats to Charmaine and 3/7 of the remaining nougats to Vanessa. Given that she was

Question

left with 4/9 of the original number of nougats, how many nougats did she give to Vanessa?

Answer 1

Let's say Rachel initially had x nougats.
After giving 8 nougats to Charmaine, Rachel remained with x - 8 nougats.
Rachel then gave 3/7(x - 8) nougats to Vanessa.
Rachel was left with 4/9(x) = 4/9x nougats.
Since she gave 3/7(x - 8) nougats to Vanessa, then 4/9x = x - 8 - 3/7(x - 8).
Multiplying through the parenthesis, we get 4/9x = x - 8 - 3/7x + 24/7.
Multiplying through again, we get 28x = 63x - 504 - 27x + 216.
Grouping like terms we get 28x - 63x + 27x = 504 - 216.
Subtracting x from both sides, we get 0x = 504 - 216.
Combining like terms, we get 28x = 288.
Dividing both sides by 28, we get x = 288/28 = 72 nougats
Rachel gave Vanessa 3/7(x - 8) = 3/7(72 - 8) = 3/7(64) = 192/7 = <<3/7*64=27.42857>>27.42857 nougats to Vanessa, which is approximately 27.43 nougats. Answer: \boxed{27.43}.