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.

thanks, this helped a lot

solve 7ft to m

Yeah, and be careful! – the elevator might fall or something! =D

crap