Marcus and his twin sister Marcie decide to save 25 each week to buy a video console. How long will it take them to save 675?

Since Marcus and Marcie are each saving $25 per week, their combined savings per week is $25 + $25 = $<<25+25=50>>50.

To find out how many weeks they need to save $675, we divide $675 by $50/week, giving us a quotient of $<<675/50=13.5>>13.5 weeks.
Since we can't have half a week, we round up the number to the nearest whole number, meaning it will take them 14 weeks to save $675. Answer: \boxed{14}.