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All right master members here we go Another word problem

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for you Nicky has six grand in the bank and

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she plans on spending a hundred twenty bucks a month

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after How many months will have the money remain in

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the account if no more deposits are made Well nicky

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has a secret she's a closet goma on a budget

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She has a taste for caviar oysters on the half

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shell and those strange gelatinous formations that look like one

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thing but taste like another But such luxury doesn't come

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cheap She can't afford dinner for two at a michelin

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star restaurant so she satisfies those cravings by taking herself

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out to a fancy lunch once a month Well the

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initial value of nikki's foodie account six grand and she

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is depleting the original value of the account by one

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hundred twenty bucks in gastronomic goodness every month Because the

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same thing happens over and over and over it's a

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constant rate Any situation with an initial value in a

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constant rate can be modeled by a linear equation in

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the form Yes your friend and mine Why equals mx

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plus b emma's a slope or the rate of change

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In this case it's Ah negative one Twenty Not positive

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one twenty Because nicky's taking money out of the account

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The initial value be is the six grand she started

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with So the equation that represents the money in her

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account Why After any number of months Acts is why

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equals negative 1 twenty x plus six thousand Well why

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represents the money remaining in the account And nikki wants

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to know how many months she contrite herself before her

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account is halfway to empty or a two three grand

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So just substitute that three grand in there for why

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and solve for x we'll why equals negative one twenty

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x plus six grand right that's our core equation and

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then we can just sub So i got three thousand

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equals negative one twenty x plus six thousand then subtract

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six thousand from each side and we get three thousand

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equals one twenty x and just divide both sides by

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one twenty And there we go Twenty five is the

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right answer It's After twenty five months nora just over

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two years of secretive dining nikki will have half the 00:01:55.446 --> [endTime] money she started with Yeah what a waste No

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