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# 重量單位的應用題 (英): U06_L1_T2_we3 Application problems involving units of weight

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- A standard elevator in a mid-rise building can hold a
- maximum weight of 1 and 1/2 tons.
- Assuming an average adult weight of 160 pounds, what is
- the maximum number of adults who could
- safely ride the elevator?
- So what we need to do is we have to get the maximum weight
- that the elevator could hold in terms of pounds.
- And then say, OK, well, how many adults is that?
- So they gave us the maximum weight in terms of tons.
- So they say it is 1 and 1/2 tons.
- And it's always easier to deal with improper fractions than
- mixed numbers, so let's write this as an improper fraction.
- 1 and 1/2 tons is the same thing as-- well, 1 ton is 2
- halves, and then you add another 1
- half, that's 3 halves.
- So you get 3/2 tons.
- Or another way to think about it is 2 times 1 is
- 2, plus 1 is 3.
- So the maximum capacity is 3/2 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 per ton.
- This wasn't given in the problem anywhere.
- This is something I knew from past experience, and 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 3/2 tons 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, 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 2,000 pounds for every 1 ton, or you could just
- say 2,000 pounds per ton.
- You could put the 1 there, but it doesn't really change the
- expression.
- Now, if we multiply 3/2 tons times 2,000 pounds per ton,
- what'll happen is that the tons cancel out.
- That was the whole point of multiplying it by this.
- And we would be left with 3/2 times 2,000, and the only unit
- left is pounds.
- And if you do it this way, you'll never get confused.
- You'll 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.
- If there are 2,000 pounds per ton and there are 1 and 1/2
- tons, I should multiply 1 and 1/2 times 2,000 to get the
- number of pounds.
- That makes sense.
- And we know 1 and 1/2 times 2,000 is 3,000, but we'll
- figure it out right here.
- So what is 3/2 times 2,000?
- Well, I just told you answer.
- We can actually simplify it right over here.
- This is going to be 3 times 2,000/2 pounds.
- We can divide the numerator and the denominator by 2.
- This will become 1,000, and this will become 1, so it's 3
- times 1,000 pounds, or this is equal to 3,000 pounds.
- So what we've done so far, we've just figured out the
- maximum capacity of the elevator.
- It can hold 1 and 1/2 tons, which is the exact same thing
- as 3,000 pounds.
- Now, what we need to figure out is 3,000 pounds is the
- equivalent to how many average adults of 160 pounds?
- Or how many 160 pound people would it take to weigh a total
- of 3,000 pounds?
- Well, we can just divide by 160.
- And if you want to make sure that the units work out,
- remember, we want our answer to be in terms of people, and
- we want the pounds to cancel out.
- So we have pounds in the numerator here, so if we
- divide by pounds, the pounds will cancel out.
- And then we want our leftover to be people, or maybe person.
- Person, people, same thing.
- Let me do people.
- The grammar of it, singular, plural, 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?
- 1 person weighs 160 pounds, so there's 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.
- We're multiplying 3,000 times 1/160, but 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.
- Divide by 160.
- It tells you how many people.
- But this way, you know that the units are working out.
- So this is going to be equal to 3,000/160 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 the denominator by 10, this
- becomes 300/16.
- 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?
- We could divide by 2 again.
- Let me rewrite it.
- So this is the same thing as 150/8 people.
- 150, we can divide by 2.
- It 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 eight times.
- 8 times 4 is 32.
- Subtract.
- 5 minutes 2 is 3.
- And then you have the decimal.
- We're going to the right of the ones place.
- We're going to the tenths place now.
- So we can bring down a zero over here.
- 4 goes into 30 seven times.
- 7 times 4 is 28.
- You subtract.
- You get 2.
- Bring down another zero.
- 4 goes into 20 exactly five times.
- 5 times 4 is 20, and then we are done.
- So this expression is exactly-- the 3,000 divided by
- 160, or the 150 divided by 8, the 75 divided by 4, it all
- turns out to be 18.75 people is the
- capacity of the elevator.
- 18.75 average 160-pound people would weigh 3,000 pounds.
- Now, do 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 3/4 of a person, or
- 75/100 of a person, the maximum number
- is going to be 18.
- If you have 19 average-weight adults, you are going to be
- too heavy, and the elevator will fall or something.

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