There were some tarts in a box 5 8 of the tarts were chocolate tarts and the rest were vanilla tarts after mrs cheng sold 1 3 of the vanilla tarts there were 30 vanilla tarts left in the box how many tarts were there altogether in the box at first?

Answer 1

Let's assume that the total number of tarts at first is represented by x.
The number of chocolate tarts in the box is 5/8 of x, which is (5/8)x.
The number of vanilla tarts in the box is x - (5/8)x, which simplifies to (3/8)x.
After Mrs. Cheng sold 1/3 of the vanilla tarts, there were 30 left, so (2/3)(3/8)x = 30.
Multiplying both sides by (3/2) gives (3/8)x = 45.
Dividing both sides by (3/8) gives x = 45/(3/8), which simplifies to x = 45 * (8/3), which is x = 120.
So, there were 120 tarts altogether in the box at first. Answer: \boxed{120}.