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Alice fills up the gas tank of her car before going for a long drive the equation below it actually should be above the equation above models the amount of gas G in gallons analysis car when she is driven m miles what is the meaning of 32 in the equation all right let's look up here this is the gallons that she has left in her car and what's going on here so it makes sense that look when M is 0 when she's driven nothing she's going to have 15 gallons in her car and then you go as you drive more and more you're going to subtract more and more gallons from her car so this is this term right over here this is the number of gallons this is the number of gallons used up so what is why are you dividing if you have m miles divided by 32 how do you get gallons what are the units on the 32 need to be and so let's just think about this if I have miles so this is miles up here and I'm gonna be dividing them by some mystery units some mystery units I need to get gallons I need to get I need to get gallons because this is going to be the number of gallons used up so what are the mystery units going to be well we can treat these units the way we would treat algebraic algebraic variables so let's listen we could solve for units here so we could take the reciprocal of both sides and we could say the unit's the mystery units divided by miles is going to be 1 over gallons or I guess you say per gallon it's gonna be one over gallons and then multiply both sides times miles multiply both sides times miles you're going to get the mystery units the mystery units are going to be if you multiply both sides by miles and it's I don't want to get confused with this over here so we multiply both sides by miles both sides by miles your mystery units are going to be miles miles per gallon so this right over here the unit's over here in order for this thing to be to come out two miles in order to come up two gallons this in the numeral have em miles / 32 miles-per-gallon miles per gallon this is telling you the how much mileage you get per gallon for her car how much she is getting so look at the choices Alice uses 32 gallons of gas per mile we have to be very careful its miles per gallon not gas per mile Alice's tank can hold 32 gallons of gas no Alice's tank can hold 15 gallons of gas gas that she fills up her tank and before she's driven anything she we see here when M is zero she's gonna have 15 gallons in her car so that's not right Alice can drive 32 miles on a tank of gas that's right the units here are 32 miles per gallon so that's that one Alice's car could drive 32 miles to the gallon oh yeah that was that was that was a close one this isn't 32 miles per gallon this is 32 miles on a tank of gas this would be 32 miles on over 15 gallons no no that's not right I was that was a close one Alice's car can drive 32 miles per gallon that's right 32 miles 32 miles per gallon and if this is a unit business that I just did thought you find it confusing one other way to think about it I mean you could have ruled you could have ruled out something like this cuz when you look at this you could see that okay her tank holds 32 holds her her tank holds 15 gallons is you could have you could have tried you could have tried this one and you would have seen that the units didn't work out if you have 15 gallons 15 gallons - M miles / 30 to 32 gallons per mile 32 gallons per mile what would the unit's end up being here less special ear aight over here you would have miles / McGowan's per mile this is going to be this is going to be minus M times I guess let me write it this way M over 32 miles times miles per gallon miles / miles per gallon you get miles squared per gallon you get all these you'd get these crazy units up here so hopefully it makes sense that we would pick this this last choice and this one almost got me when they said tank of gas I was thinking I'm brain was thinking gallon I want I was so already programmed for the answer but anyway yes this is the last the last choice is what we want to go with