Main content

### Course: Praxis Core Math > Unit 1

Lesson 4: Algebra- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example
- Algebraic word problems | Lesson
- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Algebraic word problems | Worked example

Sal Khan works through an algebraic word problem question from the Praxis Core Math test.

## Want to join the conversation?

- At the end of a snow storm, Elijah saw there was a lot of snow on his front lawn. The temperature increased and the snow began to melt at a steady rate. There was a depth of 18 inches of snow on the lawn when the storm ended and then it started melting at a rate of 1.5 inches per hour. Write an equation for S,S, in terms of t,t, representing the depth of snow on Elijah's lawn, in inches, tt hours after the snow stopped falling.(4 votes)
- could you not have combined the +128 and the -192 before subtracting and/or adding them to the other side? thank you.(3 votes)
- I did:

16 x 8= $128

320-128= 192

192/24= 8

Still trying to figure out where I went wrong... 👀(2 votes)- 16 x 8= $128

320-128= 192

192/24= 8, but then this is how many hours he worked extra. You have to answer to the question how many hours long was THAT SHIFT. It will be 8+8=16(2 votes)

- Soooo how would I solve... A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?

Im kinda confused(2 votes) - Hello I Java a question?(1 vote)
- Why did you do x-8 why 8

The 8 is gone bcz 8 multiple by 16

So all of the hours is gone so why 8(1 vote) - if the world is spinning why is the sky so clear?(0 votes)
- A long distance phone call costs $10.00 for the first ten

minutes and $0.75 for each additional thirty seconds.

If Andre has $16.65, he can talk for(0 votes)- idk i think its $10.00(1 vote)

## Video transcript

- [Instructor] Alfonso earns $16 per hour for the first eight hours of his shift. For each additional hour he works beyond the first eight
hours, he earns $24 per hour. If Alfonso earned $320
from a single shift, how many hours long was that shift? Pause this video, see if
you can figure this out. Okay, now let's do this together. So let's remind ourselves,
they want us to figure out how many hours long was Alfonso's shift? So let's just make that what
we're trying to figure out. Let's say that x is equal to the number of hours of the shift. So if the shift is x hours long, how much would Alfonso make? Well, we can see that he's
working more than eight hours because eight times 16, you might be able to do that in your head, but it's nowhere close to $320. So he definitely worked
more than eight hours. So he's going to make $16 per hour, times the first eight hours, and then plus, then he's
going to make $24 per hour, times the remaining hours. Now what's going to be
the remaining hours? You might be tempted to say x, but x would be his total shift. But we're saying the remaining hours after he works the first eight hours. So the remaining hours
would be x minus eight. So for example, x were 12, he's gonna make $16 an
hour for eight hours, and then 12 minus eight, he's going to make $24 for
the remaining four hours. And so this expression right over here, this is going to be the total amount that he's going to make for the shift, and they tell us that is $320. And that is going to be equal to $320. And so now we have this
algebraic expression and we can solve for x. The number of hours of his shift. So 16 times eight, you can
use a calculator for that, but you might be able
to do it in your head, eight times six is 48,
plus eight times 10 is 80. So that is 128, plus, now we can distribute this 24. 24 times x and then minus 24 times eight. So let's see, 20 times eight is 160. Four times eight is 32, so it's minus 192. And once again, you can use a calculator on the practice if you don't
feel comfortable doing that or if you don't want to do it on paper. In fact, I encourage
you to use a calculator if you feel a little bit uncomfortable. And that's going to be equal to $320. And like we've seen before, we want to isolate the xs
on one side of the equation. So we can get rid of this
128 and this negative 192 by subtracting 128 and adding 192. Now of course, if we do
that on the left-hand side, we have to do that on
the right-hand side too. So we can, well we can add 192 and then we can subtract 128. And I did all of that in one step. I'm just adding and
subtracting the same amount from both sides. So on our left-hand side
we're just left with a 24x, and then our right-hand side,
you could do this by hand, but I keep talking about a calculator, so let me just get a
calculator out and do it. So you have 320 plus 192, minus 128, is equal to 384. And we're going to have to divide by 24. Actually, let me just do that. So this is going to be 384. Now to solve for x, you just
divide both sides by 24, and we get x is equal to, I'll
just get the calculator out. Again, just take that and divide by 24. We get 16, x is equal to 16 which is that choice right over there. Now there might have been
another way to do this. You could've tried out values. You could said, okay, if
Alfonso works eight hours, well that's too little. 10 hours, and keep trying values where for the first eight
hours, you do 16 times that. 16 times eight, and then after that, you each incremental hour's $24 an hour. So it depends which strategy
works better for you. But the algebraic way, we'll
definitely, if you do it in a logical way it'll definitely
get you to the right end.