Ken and Ben have the same number of sweets. Ken ate $\frac{1}{2}$ of his sweets and gave $\frac{1}{2}$ of his remaining sweets to Ben. After that, Ben has 35 sweets. How many sweets did Ken have at first? Ans: ___

1. Determine the fraction of Ken's original sweets given to Ben

Ken ate $\frac{1}{2}$ of his sweets, so he had $1 - \frac{1}{2} = \frac{1}{2}$ remaining.
He gave $\frac{1}{2}$ of his remaining sweets to Ben.
Fraction given to Ben = $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ of Ken's original sweets.

2. Set up the relationship for Ben's sweets and solve for Ken's original amount

Let Ken's original number of sweets be $4$ units.
Ben also had $4$ units at first.
Ben received $1$ unit from Ken.
Ben's final amount = $4 \text{ units} + 1 \text{ unit} = 5 \text{ units}$.
$5 \text{ units} = 35$
$1 \text{ unit} = 35 \div 5 = 7$
Ken's original amount = $4 \text{ units} = 4 \times 7 = 28$.