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## Heart of algebra

# Linear equation word problems — Basic example

## Video 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.