Estimating graphically with systems in real world problems
About this video
The video compares two soil delivery services by graphing their costs. GreenHaul costs $25 plus $4 per bag and EarthMove costs y = 5x + 15; the lines meet at 10 bags ($65), so EarthMove is cheaper for fewer than 10 bags and GreenHaul is cheaper for more than 10.
You'll be able to
- graph a cost line from a starting fee (y-intercept) and a cost per item (slope).
- use the intersection of two lines to compare two options.
- decide which option is cheaper for a given number of items.
Key words
- delivery fee
- A fixed cost paid no matter how many bags you order; it is the y-intercept.
- rate per bag
- The extra cost for each bag; it is the slope of the line.
- point of intersection
- Where two lines cross; here both services cost the same.
Transcript
- [Instructor] We're told, "A community garden is deciding which delivery service to use to bring soil to the site. The total cost depends on the number of bags of soil ordered. GreenHaul charges a $25 delivery fee and $4 per bag of soil. EarthMove charges a $15 delivery fee and $5 per bag of soil.
Here's a graph of the total cost of an order from GreenHaul." So let's see, GreenHaul was a $25 delivery fee, $4 per bag of soil. And let's see, it looks like, yes, just to get 'em deliver, it's $25, and then let's say if I were to get 10 bags of soil at $4 per bag, that should be another $40.
And yes, it looks like it got us to $65. So that is the appropriate slope here. So the slope of the GreenHaul line is 4. So now they ask us, "Estimate the graph of EarthMove's cost, given by y = 5x + 15, to determine the statement that compares the two costs more accurately."
And we have a bunch of choices here, but what I'm gonna do is actually just try to graph EarthMove's graph. So they gave us an equation, but we can see that at zero bags, we're gonna pay the $15 delivery fee. And then our slope is essentially going to be 5. Every time we add a bag of soil, we're gonna add $5 of cost with EarthMove.
So let me graph that. So we're gonna start at 15, right over there, and our slope is going to be 5. So one way to think about it is if I add 10, I should add 50 to that, which should get me to 65. And actually, that got me right to that point of intersection. But that looks like I've graphed EarthMove.
And so before I even look at the choices, it looks like if I order less than 10 bags of soil, our EarthMove is better, and if I order more than 10 bags of soil, I get a better price from GreenHaul. Remember, a better price would be a lower cost in terms of dollars.
This axis is number of bags. Vertical axis is cost in dollars. So let's look at the choices. For more than 10 bags of soil, GreenHaul is cheaper. For more than 10 bags of soil, GreenHaul indeed is cheaper. Green Haul, remember that's the graph that was already there, not the one that I just graphed.
It's the green one. So that makes sense. So I like that one. For more than 10 bags of soil, GreenHaul is cheaper. For more than 10 bags of soil, EarthMove is cheaper. That's not right. For more than six bags of soil, GreenHaul is cheaper. Six bags of soil, well, no, it depends.
Right at 6 bags of soil, GreenHaul is more expensive, but if you get a lot more than six, in particular, more than 10, you can see that GreenHaul is cheaper. So I don't like that one. And then for more than six bags of soil, EarthMove is cheaper, that's true, right at six bags and a little bit higher up till 10, but then beyond 10, it's not true, so I don't like D either.
So I definitely like choice A.
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