Buying a 2nd home and mortgage question?

My husband and I currently own a home in CT and if we sold it, we would like to sell it for $ 200,000 (we currently have a 30 yr. fixed mortgage with a balance of about $ 152,000). We would be relocating to MO where homes are much cheaper, and lets say we purchase a home for $ 145,000. Would we be able to take the sale price of our CT home and apply it to the MO home and not take out a mortgage? Or are you only entitled to the equity amount that your home is worth after selling, being that we are mortgaging $ 152k? Also, when purchasing your 2nd home do you need to go and secure a new mortgage with a different interest rate or can you keep your current mortgage and change the terms?

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