Linear function word problems — Basic example
About this video
Works through a word problem about two TV shows. Show A has 11-minute episodes and show B has 43-minute episodes, and together they add up to 196 minutes. The video builds the equation step by step, multiplying each episode length by the number of episodes watched, and adding the two totals to get 11a + 43b = 196.
You'll be able to
- represent a total time as a sum of episode length multiplied by the number of episodes
- write a linear equation from a word problem with two unknowns
- explain what each variable in the equation represents
Key words
- Variable
- A letter, such as a or b, that stands for an unknown quantity, here the number of episodes watched.
- Linear equation
- An equation in which each variable is raised to the first power, such as 11a + 43b = 196.
- Coefficient
- The number multiplied by a variable, such as 11 in 11a, which here is the length of each episode in minutes.
- Total time
- The sum of all time spent watching, which must equal the 196 minutes given in the problem.
Transcript
- [Instructor] We're told Fara watched two different TV shows last week. TV show A has 11-minute episodes, and TV show B has 43-minute episodes. Together, she spent 196 minutes watching TV shows. Which equation models this relationship, where lowercase a is the number of TV show A episodes and lowercase b is the number of TV show B episodes Fara watched?
So pause this video and have a go at it on your own before we work through this together. All right, now, let's do this together. So we know that together, she spent 196 minutes watching TV shows. So what we wanna do is total the amount of time she spent watching TV show A, the amount of time she spent watching TV show B, and then that should be equal to 196.
And so, actually, let me just do TV show A in this orange color. How much time did she spend watching TV show A? Well, we know that each episode of TV show A is 11 minutes. So it's going to be 11 minutes times the number of episodes. And they said that lowercase a is the number of TV show A episodes.
So this right over here, 11a, is how much time she spent watching TV show A. And what about TV show B? Well, each episode is 43 minutes. So it's going to be 43 minutes per episode. And how many episodes are there of TV show B? Well, it's lowercase b is the number of TV show B episodes.
So 43 minutes per episode times lowercase b episodes, that's how much time she spent watching TV show B. So if you add the amount of time she watched TV show A to the amount of time she spent watching TV show B, that will be her total time, and we know that that needs to be equal to 196.
And so let's see which of these choices have it. That's not that one. Let's see, this one is it, exactly what we got. This is different, and this is different. And we're done.
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