A quick glance at amazon.co.uk shows high-wattage induction cooktops that are relatively cheap, e.g.
https://www.amazon.co.uk/GIONIEN-Domino-Induction-Hob-Electr... is a dual-burner 3500W model that takes 220V-240V (unclear if it's ok on 208V?) for £109.99 (USD$143). 60 Hz would be a leap of faith, but is probably fine.
Not $50, but still.