yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Modeling with multiple variables: Taco stand | Modeling | Algebra 2 | Khan Academy


2m read
·Nov 10, 2024

We're told a certain taco stand sells t tacos per day for a net profit of 300. Each taco costs c dollars to make and is sold for p dollars. Write an equation that relates t, c, and p, so pause this video and see if you can do that.

All right, now let's work this together. So let's just remind ourselves what's going on here. We have the number of tacos sold per day is t, so t equals the number of tacos sold per day. They tell us net profit of 300, so we could say 300 is equal to net profit. They tell us that each taco costs c dollars to make, so c is equal to cost per taco. And then p is what each taco is sold for; right over there is sold for p dollars, so p is equal to the price per taco.

So how do we figure out what the net profit is going to be? Well, we could write it this way: net profit is going to be equal to the total amount of money that you bring in minus the total amount of money that you have to spend. So what is going to be the total amount that you bring in? What's going to be the amount you sell times what's going to be the number of tacos you sell times the price per taco? So t times p, this is how much money you're bringing in.

But of course, you have to also subtract out your cost. Well, what's going to be your cost? What's going to be the number of tacos times the cost per taco? That's how much we're going to spend, so the number of tacos times the cost per taco. Now, here I've written everything as variables. Well, I wrote net profit out, but they told us that net profit is equal to 300. So I could write it like this: 300 is equal to t times p, I'll do those same colors, t times p minus t times c minus t times c.

Now, it's completely possible that they didn't give us net profit as 300 per day; instead, they said that is one of the variables and they gave one of the other variables. And that would have been okay. We could have used the same logic. Whatever they didn't give us, we could have set up as a variable, and whatever they did give us, maybe they gave us the price per taco; we could have put that as a given number.

Now, I know what some of you all are thinking. You didn't get exactly this. You might have thought about it the other way. You might have thought about it as the profit is going to be equal to the number of tacos times the profit per taco. And what's going to be the profit per taco? Well, that's going to be how much each taco is sold for minus how much each taco costs. And this also would have been completely credible.

And if you look at these two, they're actually algebraically equivalent. If you factor out t here, you get this expression on the right.

More Articles

View All
Ray Dalio & Bill Belichick on Going from Nothing to Something Big: Part 2
And then communicating well, because when I went from the 67 who knew me and knew where I was coming from, and then I had to go to another level, how was I going to keep that same communication, that same idea of meritocracy? That’s why I started to write…
This Video Will Make You Angry
Hello Internet. Thoughts compete for space in your brain: cat photos, news stories, belief structures, funny GIFs, educational videos, not-so-educational videos, and your thinking inventory is limited. A thought without a brain to think it dies. Now we ca…
From Broke To Bugatti | Inside The Millionaire Empire Of Doug DeMuro
This is the like button, and you should hit it. So when you think of a self-started multi-million dollar business that’s accumulated one and a half billion views and outpaces the ranks of even the top-rated television hits, your mind doesn’t think of this…
Sigma Male Or Joker? (animated)
The Sigma male is the hierarchical chameleon that shape-shifts himself through life, and by his very nature, does not belong anywhere. Because the Sigma male rather sees human existence as a game, he sometimes chuckles a bit when he sees people taking lif…
Michael Burry's Controversial Bet for 2024.
Well, Michael Barry is back. He has just released his latest 13F filing, and in it, it shows that he has been on quite the buying spree in Q4 of 2023. He opened 18 new positions, added to two, reduced in five, and sold four. So, in this video, we’re going…
Worked example identifying experiment | Study design | AP Statistics | Khan Academy
So we have some type of study described here. I encourage you to pause this video and think about whether this is an observational study, an experiment, or a sample study. Also, think about whether it was conducted well. All right, now let’s do this toge…