Julie bought a house for $315,000 and has a $285,000 mortgage. she claims she has $315,000 in equity. is she correct? if not, how much home equity does she have? explain.

No she is not. Equity is equal to assets less liabilities. Her asset is the house market value and her liability is the payable mortgage amount of the house.
where
 asset = $315000
 liability = $285000

Julie's Home equity =  asset - liability
                                = $315000- $285000
                                = $ 30000

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