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