Linear equation word problems — Basic example
About this video
Kaylee plans how many classes to take, with each class needing 2 1/2 hours of homework per week and a fixed 6 1/2 hours of reading shared across all classes. The video builds the equation 2 1/2 C + 6 1/2 = 19 from the 19 available hours, and rules out the distractors by checking what each term means.
You'll be able to
- translate a word problem about time into a linear equation.
- tell which quantities scale with the number of classes and which stay fixed.
- check candidate equations by testing what each term means in context.
Key words
- Variable
- A letter that stands for an unknown quantity, here C for the number of classes.
- Coefficient
- The number multiplying a variable, such as 2 1/2 in 2 1/2 C.
- Linear equation
- An equation in which each variable appears to the first power, such as 2.5C + 6.5 = 19.
- Constant term
- A fixed number that does not depend on the variable, such as the 6 1/2 reading hours.
Transcript
- [Instructor] Kaylee wants to do well in her classes, so she is budgeting her time carefully to decide the number of classes, C, she will take this year. For each each class that she takes, she expects to spend 2 1/2 hours each week working on homework. She expects to spend an additional 6 1/2 hours each week completing the assigned reading for all of her classes together.
If Kaylee has 19 hours available each week to complete homework and reading for her classes, which equation best models the situation? Alright, so she has a total of 19 hours available. She has 19 hours available. She has 19 hours available each week to complete homework and reading for her classes.
So how much time is it going to take her to complete the homework? Well it says that she expects to spend 2 1/2 hours each week working on homework for, well actually I should say over here, for each class that she takes, she expects to spend 2 1/2 hours each week working on homework.
Let me underline that. For each class that she takes, she expects to spend 2 1/2 hours each week working on homework. So that's going to be 2 1/2 hours each week per class. Now how many classes is she taking? Well she's gonna take C classes. So the total amount that she spends on homework, so the amount that she spends on homework is going to be 2 1/2 times C, up in parentheses just to make it clear what I'm doing here.
So it's gonna be 2 1/2 time C is the amount of time she spends on homework. And how much is she going to spend on reading? Well, it says over here she expects to spend an additional 6 1/2 hours each week completing the assigned reading for all of her classes together.
So this sentence says it doesn't matter how many classes she takes, she's gonna spend 6 1/2 hours reading. So, it's not dependent on the number of classes she takes. So this is the amount of time she's just gonna spend reading. And so the amount she spends on homework plus the amount she spends on reading need to add up to 19 hours.
So which of these choices are what I just wrote over here? So let's see, they have the 19 on the other side but you see they have 2 1/2 C minus 6 1/2, no that's not this right over here. 2 1/2 C plus 6 1/2, yup that's what we have over here, is equal to 19, yup that's this choice.
The only difference between this and what I wrote is they just swapped the two sides of the equality which you can always do. These other choices, let's see 6 1/2 times C, well this would imply that you're spending 6 1/2 hours per class so that's not right. And then this is also 6 1/2 times C, so that's not gonna work out either.
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