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
left with 4/9 of the original number of nougats, how many nougats did she give to Vanessa?
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}.
Let's break down the problem step-by-step:
1. Let's assume the original number of nougats Rachel bought is "x".
2. Rachel gave 8 nougats to Charmaine. So, the number of remaining nougats is "x - 8".
3. Rachel gave 3/7 of the remaining nougats to Vanessa. So, the number of nougats given to Vanessa is (3/7) * (x - 8).
4. Rachel was left with 4/9 of the original number of nougats. So, the number of nougats left is (4/9) * x.
Now, we can set up an equation to find the number of nougats given to Vanessa:
(4/9) * x = (3/7) * (x - 8)
To solve this equation:
1. Multiply both sides of the equation by 63 (the least common multiple of 9 and 7) to eliminate the fractions:
(4/9) * x * 63 = (3/7) * (x - 8) * 63
2. Simplify:
28x = 27(x - 8)
3. Distribute:
28x = 27x - 216
4. Subtract 27x from both sides:
28x - 27x = -216
5. Simplify:
x = -216
Since the number of nougats cannot be negative, there seems to be an error in the problem statement or the calculations.
Please verify the information provided or check the calculations to proceed with a correct answer.