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CCSS.Math:

a standard elevator in a mid-rise building can hold a maximum weight of one and a half tonnes assuming an average adult weight of 160 pounds what is the maximum number of adults who could safely ride the elevator so we need to do is we have to get the maximum weight that we that the elevator can hold in terms of pounds and just say okay well how many adults is that so they gave us the maximum weight in terms of tons so they say it is one and one-half tons and it's always easier to be to deal with improper fractions and mixed numbers so let's write this as an improper fraction so one in one half tonnes is the same thing as well one ton is two halves and then you add another 1/2 that's three halves so you get three halves tons or another way to think about it is two times one is two plus one is three so the maximum capacity is three has tons let's think about how many pounds that is and to do that we have to know that there are 2,000 pounds per ton let me write this up here we know that there are 2,000 pounds pounds per ton this wasn't given in the problem anywhere this is something I knew from past experience it's a good thing to know in general that a ton is 2,000 pounds so I'm going to write it right over here now how do we convert these three half tonnes into pounds well we're going to multiply it by something and the units that we're going to multiply by we want the tons to cancel out so we're going to want to have tons in the denominator we want tons in the denominator so it cancels out with this tons up here and then we want pounds in the numerator and that's exactly what we wrote up here there are two thousand pounds two thousand pounds for every one tonne or you could just say two thousand pounds per ton you could put the one there but it doesn't really change the expression now if we multiply three half tonnes times 2,000 pounds per tonne the what will happen is that the tonnes cancel out that was a whole point of multiplying it by this and we would be left with we would be left with three halfs three halves times 2,000 times 2,000 and the only unit left is pounds is pounds and this is the way if you do it this way you'll never get confused you'll know what you're you know that the units cancel out so you're getting the right units but if you just think about it in your mind it should also make sense to if two thousand if there are two thousand pounds per tonne and they're about one and a half tons I should multiply one and a half times two thousand to get the number of pounds that makes sense it'll give me and we know one and a half times two thousand is three thousand but we'll figure it out right here so what is three-halves times two thousand when i just told you the answer we can actually simplify it right over here this is going to be three times two thousand over two pounds we can divide the numerator and the denominator by 2 this will become one thousand and this will become one so it's three times one thousand pounds or this is equal to three thousand pounds so what we've done so far if we've just figured out the maximum capacity of the elevator it can hold one and a half tonnes which is the exact same thing as three thousand pounds now what we need to figure out is three thousand pounds is equivalent to how many average adult's of 160 pounds or how many a hundred sixty pound people would it take to weigh a total of three thousand pounds well we can just divide by 160 and if you want to make sure that the units work out remember we want this we want our answer to be in terms of people and we want the pounds to cancel out so we have a pound in the numerator here so if we divide by pounds the pounds will cancel out and then we have we want our leftover to be people or maybe person person person people same thing let me do people the the grammar of it or doing singular program might make it a little confusing but I think you get the general idea now if we were to write this out what does it tell us one person weighs 160 pounds so there's one people or one person for every 160 pounds so notice if we multiply these two expressions the pounds will cancel out we'll be just left with people but we're really just dividing we're multiplying three thousand times one over 160 it's really just taking 3,000 and dividing by 160 which makes sense we have a capacity of 3,000 each of our people weighs 160 pounds divided by a hundred 60 tells you how many people but this way you know that the units are working out so this is going to be equal to this is going to be equal to 3000 over 160 people that is the maximum capacity of the elevator in terms of average people now what is this well we can divide the numerator and the denominator by 10 if we divide the numerator and denominator by 10 this becomes 300 over 16 if we divide 300 by if we divide 300 by 2 this becomes 150 if we divide 16 by 2 this becomes 8 now let's see what can we do more here well we could divide by 2 again let me rewrite it I don't this kit so this is the same thing as 150 over 8 people see 150 we can divide by 2 this gives us 75 and if you take 8 divided by 2 that is 4 so we have 75 divided by 4 people let me just do that work it out so you have 75 divided by 4 4 goes into 7 one time 1 times 4 is 4 you subtract 7 minus 4 is 3 bring down this 5 4 goes into 35 8 times 8 times 4 is 32 subtract 5 minus 2 is 3 and then you have the decimal we're going beyond the we're going to the right of the ones place we're going to the tenths place now so we can bring down a 0 over here 4 goes into 30 7 times 7 times 4 is 28 you subtract you get to bring down another is 0 4 goes into 20 exactly 5 times 5 times 4 is 20 and then we are done so this expression is exactly you know the 3000 divided by 160 or the 150 divided by 8 or the 75 divided 4 it all turns out to be 18 point seven five people is the capacity of the elevator 18.75 average 60 pound people would weigh 3,000 pounds now did they want a decimal what is the maximum number of adults who could safely ride the elevator well if they're all going to be average then the maximum number of adults since you can't have since you can't have three-quarters of a people of a person or 75 hundredths of a person the maximum number is going to be 18 if you have 19 average weight adults you're going to be too heavy and the elevator will will fall or something