Interpret proportionality constants

we can calculate the depth D of snow in centimeters that accumulates in Harper's yard during the first eight hours of a snowstorm using the equation D is equal to five times H so D is the depth of snow in centimeters H is time that elapsed is in hours how many hours does it take for one centimeter of snow to accumulate in Harper's yard pause this video and see if you can figure that out all right so we want to figure out what H gives us a D of 1 centimeter remember D is measured in centimeters so we really just need to solve the equation one centimeter when D is equal to 1 what is H going to be and to solve for H we just need to divide both sides by 5 so you divide both sides by 5 the coefficient on the H and you are left with H is equal to 1/5 and the unit for H is hours 1/5 of an hour so 1/5 of an hour if they had minutes you there then you would say well 1/5 of an hour there are 60 minutes we'll use just 12 minutes but they just want it as a as a number of hours so 1/5 of an hour how many centimeters of snow accumulates in per hour all right this is a little bit of a typo how many centimeters of snow accumulate in in we could say one hour in one hour or they could have said how many centimeters of snow accumulate per hour that's another way of thinking about it so we could get rid of per hour so pause the video and see if you can figure that out well there's a couple of ways to think about it perhaps the easiest one is to say well what is D when H is equal to 1 and so we could just say D when H is equal to 1 when only one hour has elapsed well it's going to be 5 times 1 which is equal to 5 and our units for D are in centimeters so 5 centimeters let's do another example Betty's bakery calculates the total price D in dollars for C cupcakes using the equation D is equal to 2 C what does 2 mean in this situation so pause this video and see if you can answer this question so remember D is in dollars 4c cupcakes now one way to think about it is what happens if we take D is equal to 2 times C what happens if we divide both sides by C you have D over C is equal to 2 and so what would be the units right over here well we have dollars D dollars over C cupcakes so this would be 2 dollars because that's the units for D per cupcake dollars per cupcake this is the unit rate per cupcake how much do you have to pay per cupcake so which of these choices match up to that the bakery charges $2 for each cupcake yeah two dollars per cupcake that looks right the bakery sells two cupcakes for $1 no that would be two cupcakes per dollar not two dollars per cupcake the bakery sells two types of cupcakes no no we're definitely not talking about two types of cupcakes they're just talking about cupcakes generally I guess I guess they're one type of cupcake we don't know but just cupcakes generally is two dollars per cupcake