Yes. UW’s Housing and Food is 4K/year cheaper than Chicago’s.
https://admit.washington.edu/Paying/Cost#freshmen-transfer
Regarding the length of attendance OP has mentioned she/he may want to graduate in two years in UW so a shortened attendance in Chicago is an option.
I have heard many Chicago’s students graduate in three years plus one or two quarters nowadays. Let’s say OP takes 11 credits per year for three years she/he will have 33 credits (16 Bio + 10 Core + 7 electives). If she/he places out 8 Core credits and uses 4 AP credits for electives then she/he will have 33+8+4=45 > 42 required to graduate.
I do not say OP should do it if she/he chose Chicago but it is definitely possible without a very challenging schedule.