Since the price of each product is x dollars, R products would've costed Karen x*R dollars. Since she sold 50% of these R products for y dollars, she would've made R/2*y=Ry/2 dollars. Now these Ry/2 dollars subtracted to the total cost of the R products would represent the profit that Karen made and we know that this profit would be 2*x*R since it's 2 times the cost of the R products. With this said, our algebraic expression would be:

Ry/2-xR=2xR.

she first bought R products at x$/prod = Rx
She then sold half her products at y$/prod = 1/2Ry

we know that she profited (sell-cost) 2x the price she originally paid, which is x per product. so if she buys at 10 she sold at 30 (profit is 2x buy price) so
y-x = 2x, or y=3x

so total is -Rx + 1/2R*3x
= 1/2Rx