A vendor sold 7/5 of fruits to motorists and 1/4 to students. He also sold 3/7 of the remaining fruits to others. If the vendor was left with 168 fruits, how many fruits were sold to students?
The vendor sold a total of 1 - 7/5 - 1/4 = 20/20 - 28/20 - 5/20 = 1/20 of the fruit to others.
The total quantity of fruits sold to others is 3/7 x 1/20 = 3/140 of the fruits.
The total quantity of fruits the vendor had was 140 + 168 = <<140+168=308>>308.
Hence, the vendor sold 308 x 5/20 = <<308*5/20=77>>77 fruits to others.
Thus, the vendor sold 308/20 x 1/4 = <<308/20*1/4=7.7>>7.7 fruits to students.
Rounding off 7.7 to the nearest whole number, the vendor sold <<8=8>>8 fruits to the students. Answer: \boxed{8}.
Let's solve this step-by-step.
1. Let's assume the total number of fruits the vendor started with as "x".
2. The vendor sold 7/5 (or 1 2/5) of the fruits to motorists.
So, the number of fruits sold to motorists = (7/5) * x = 7x/5.
3. The vendor sold 1/4 of the fruits to students.
So, the number of fruits sold to students = (1/4) * x = x/4.
4. The remaining fruits after selling to motorists and students = x - (7x/5) - (x/4).
Simplifying the expression, we get: (20x - 28x - 5x) / 20 = -10x/20 = -x/2.
5. The vendor sold 3/7 of the remaining fruits to others.
So, the number of fruits sold to others = (3/7) * (-x/2) = -3x/14.
6. After selling to others, the vendor was left with 168 fruits.
Therefore, (-x/2) - (-3x/14) = 168.
Simplifying the expression, we get: (-7x - (-3x))/14 = -4x/14 = -2x/7 = 168.
7. Solving the equation -2x/7 = 168 for x:
Multiply both sides by 7 to remove the denominator: -2x = 1176.
Divide both sides by -2: x = 1176 / -2 = -588.
Since the number of fruits cannot be negative, this result is not valid.
Hence, there might be an error in the problem statement or the calculation.