If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Integrated math 1>Unit 3

Lesson 3: Word problems with multiple units

# Using 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.

## Want to join the conversation?

• 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.
• 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
• when will we ever need to use this in the real world?
• 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.
• 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.
• we could've just easily done this in our head without dimensional analysis
• 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.
• 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)
• Whats the equation for solving all problems like this?
• how to do it
(1 vote)
• 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.

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.

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.

Hope this helps!

Happy Learning!

Angelina
(1 vote)
• IMO, the fact that the factory is open 5 days per week is not 'extra information'.
The final answer of 10,000 (dollars) is truly 10,000 (dollars/workday).
What we need is value per day in general, workday or not...

Then the info of 5 (workday/week) becomes important.

i.e.
5 (workday/week) = 5 (workday/7 days) = 5/7 (workday/day)

further,
value per day (dollars/day)
= 10,000 (dollars/workday) * 5/7 (workday/day)
= (5/7) * 10,000 (dollars/day)

Which should be the correct answer (IMO).
(The 'dimensional analysis' points to this as well)
(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?