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Course: Algebra 1 > Unit 3
Lesson 3: Word problems with multiple unitsUsing units to solve problems: Toy factory
In word problems that involve multiple quantities, we can use the units of the quantities to guide our solution. In this video, we find the value of toys produced at a factory using information that involves many different quantities, not all of which are useful for our problem. Created by Sal Khan.
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Or we could just say:
1 worker makes 25 toys. We have 40 workers, so that means they all make 1,000 toys. Each toy costs 10$, so that's just 1,000 times 10 which is 10,000. No unit conversion or "canceling out" needed.
Of course, you should use dimensional analysis for more complex problems, like in Chemistry, but for this you can do it in your head in under 20 seconds. Just make sure your answer makes sense.(22 votes)
Hi! What Sal did is actually wayyy more efficient than just multiplying, because in more complex algebra problems you need this so it is definitely not useless(3 votes)
when will we ever need to use this in the real world?(3 votes)
I would think that the 5 days a week would be important since the factory produces no toys on weekends the average production per day would be lower, 7143/day to be exact. This value is more useful I think because to find the number of toys in a given amount of time you would only need to multiply by that number instead of making a separate calculation.(4 votes)
So let's say you have a problem with (2 grams[3 atoms/6 grams]) What would the final unit of be?(1 vote)- answer will be 1 atom. since grams cancel out and we are left with just atom.(6 votes)
why did 25 toys per day change to 25 toys per workers?(1 vote)
A worker produces 25 toys per day.
25 (toys / day) * 1 (day / worker)
= 25 (toys / worker)(6 votes)
we could've just easily done this in our head without dimensional analysis(2 votes)
Yes, it would be simpler to just do 10*25*40 but the dimensional analysis helps us what is going on in the problem. Most problems will force you to do that because of the different units. Basically he did that so we can learn it with easier problems before the harder ones.(3 votes)
Whats the equation for solving all problems like this?(2 votes)
Using units in algebra can be very helpful in solving problems, especially in physics and engineering.
Here’s a general approach:
Identify the units for each quantity:
In any problem, the first step is to identify what units are associated with each quantity in the problem. For example, if you’re dealing with a speed, the units might be meters per second.
Convert units if necessary:
If the units of the quantities in the problem are not consistent (for example, if one quantity is given in meters and another in kilometers), you may need to convert some quantities to consistent units.
Carry units through your calculations:
When you perform calculations, carry the units along with the quantities they’re associated with. This can help you check your work and make sure your answer makes sense.
Check that your answer is in the correct units:
Your final answer should be in the units that the problem asks for. If it’s not, you’ll need to convert it to the correct units.
Here’s an example:
Suppose you’re asked to find out how long it takes for a car to travel 100 kilometers if it’s moving at a speed of 50 kilometers per hour.
Identify the units:
The distance is in kilometers and the speed is in kilometers per hour.
Convert units:
In this case, the units are already consistent, so no conversion is necessary.
Carry units through your calculations: Time = Distance / Speed = 100 kilometers / 50 kilometers per hour = 2 hours.
Check your answer: The problem asked for a time, and your answer is in hours, so no further conversion is necessary.
Hope this helps!
Happy Learning!
Angelina(1 vote)
- At 7 A.M. a plane leaves Boston, Massachusetts, for Seattle, Washington, a distance of 3000 mi. One hour later a plane leaves Seattle for Boston. Both planes are traveling at a speed of 300 mph. How many hours after the plane leaves Seattle will the planes pass each other?(0 votes)
12:54Video transcript
- [Narrator] We're told
a factory makes toys that are sold for $10 apiece. The factory has 40 workers, and they each produce 25 toys a day. The factory is open five days a week. What is the total value of toys the factory produces in a day? Pause this video and see
if you can figure that out. All right, so let's
just think about a day, before I even look at this information. If I could figure out the value per toy, and then multiply that
times the number of toys, number of toys produced in a day, then we would have the total value. And let's see if they
give us that information. Well the value per toy,
they say the toys are sold for $10 apiece, so we
could write this this way. 10 dollars per toy, and then they do tell us, or they give us the information
that we need to figure out how many are produced in a day. We have 40 workers, and they
each produce 25 toys a day. So the amount that's produced in a day, is going to be 40 workers times 25 toys per worker. Now I could say 25 toys
per worker per day, and that makes the units
a little complicated, or I could just realize
that this entire expression I'm creating is talking about one day. So the total number of
toys produced in a day is going to be the
product of these things. And we can say that the units work out, just to make sure that we're
getting in the right direction. A toy in the denominator cancels out with the toys in the numerator, workers, when you multiply it, this
would be in the numerator, this in the denominator. So workers, workers cancel out. And so I'm gonna be left with
10 times 40 times 25 dollars. And I do want it written in dollars. And so this is going to be
equal to 10 times 40 is 400, and then 400 times 25, let's
see, that's going to be 4 times 25 times 100 so
that's 100 times 100, which is 10,000, and then the units we're left with is dollars. And now you might be
saying, wait, we didn't use all of the information and
that's true, we didn't use the fact that the factory
is open 5 days a week. We didn't need to use that information. That would have been useful if they said, what is the total value of toys the factory produces in a week. Then we would have said their
value per day is $10,000, and we could even write
it this way, per day, and then multiply that
times 5 days in a week, and that would have
given us the total value of the production in a week. But that's not what they're asking for, so we don't need that other information, and so we don't have to go to that step. And so this is really
just extra information, probably to distract you a bit.