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Course: Get ready for AP® Calculus>Unit 4

Lesson 1: 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.

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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.
• 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)
• The question is imprecise.
It should ask for the total value of toys produced in a work day, not a day. On a non-work day the factory generates 0 value.
And if you want to find the average value of toys produced in a day you have to multiply 10,000 by 5/7.
• you have been here for a while just sit a while and vibe with me
• 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.