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Last week, in Number Sense 31, we made a graph of a more continuous function: how much grass a herd of goats might eat each hour. We also took a look at what the graph might look like if it were an inequality, rather than a strict equality.  This week we are going to solve a problem using a graph.

Last week we introduced a herd of goats. Why are we keeping goats, anyway? They are cute, that's true, but they are also a lot of trouble. Well, in addition to the pleasure of their company, we get goat milk. It's a herd of dairy goats. Our herd produces 20 liters of goat milk per day. We use some of it as liquid milk: some goes in our coffee, some we drink, some we feed to the baby goats. We use the rest of the milk to make cheese.

Here is our first equation:

Liquid milk + cheese milk = 20 liters

If we call liters of liquid milk “x”, and liters of cheese milk “y” then x + y = 20.

We also know that we use more milk to make cheese than we use as liquid milk, and we have measured how much more: 4 liters.

Here is our second equation:

Cheese milk - liquid milk = 4 liters

or

y – x = 4

We want to know how much milk is used to make cheese every day.

We can use these equations to put two lines on the same graph

We can make a T chart for the first equation,

x + y = 20

and we will pick x = 0 and x = 20 for our x values,

which makes figuring out the y values super easy, since the two numbers must add up to 20.

Here is the graph of the different amounts of milk we could use for cheese and as liquid milk, given that the total amount of milk is 20 liters. If you check any spot on that line: (18, 2), (10,10), where ever... the two numbers add up to 20.

Now we will make a T chart for our second equation

y – x = 4

We will pick x = 0 and x = 10 for our t chart values, again choosing numbers that make y easy to calculate

We plot these two points on our graph, and draw a line that goes through both points

The green line shows all the solutions to cheese milk is four more liters than liquid milk, including the extreme case of zero liters of liquid milk. If we add up the total liters of milk using the green line, we will get different amounts of milk.

The spot where the green line crosses the red line, though, it the spot where the total number of liters is 20.

That says we use 12 liters of milk for cheese, 8 liters of milk as liquid milk.

12 + 8 = 20, so our first condition (20 liters per day) checks out. 12 – 8 = 4, which satisfies our second condition (four more liters used to make cheese).

Have fun in the comments

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#### 13comments | Permalink

• ##### Tips for goat cheese(10+ / 0-)

Sorry for the large image file sizes. My windows box, which I usually use for these diaries, is on the fritz, and I'm using my Ubuntu box, which doesn't have nearly the number of toys (useful programs) installed yet, since I don't use it as much.

So Irfanview, which has a nice plugin to reduce image file sizes for the web, wasn't available, and I haven't had time to find a Ubuntu application that does the same thing, although I am pretty sure there is one out there somewhere. If anyone knows of such an app for Ubuntu, please mention it in the comments. Thanks.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

• ##### Gimp will allow you to rescale an image (4+ / 0-)
Recommended by:
vcmvo2, Orinoco, jessical, Larsstephens

as well as annotate, etc.  I use it all the time...

There may be lighter programs, maybe Gwenview, since Gimp works for most of what I do I haven't looked for another.

• ##### example(4+ / 0-)
Recommended by:
vcmvo2, Orinoco, jessical, Larsstephens

• ##### Thanks, I'm sure I've got Gimp on Ubuntu(3+ / 0-)
Recommended by:
palantir, jessical, Larsstephens

but I'm pretty sure that Irfanview plugin was doing more than just resizing. The file sizes I got were tiny. It optimized the pallet, used a more efficient compression engine, maybe other things that were invisible to an end user.

Anywho... I'm temporarily back on a Windows laptop, because I messed up Ubuntu trying to get it to recognize two screens. Now I have to reinstall, because it hangs when booting.

If it's not one thing, it's another. I also have a brand new cold for the holiday break.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### I don't think Gimp is a standard package(3+ / 0-)
Recommended by:
Orinoco, jessical, Larsstephens

but it is available

apt-get install gimp

• ##### It's not(3+ / 0-)
Recommended by:
palantir, jessical, Larsstephens

but I use it a lot, so I routinely install it, along with OpenOffice.org, opera, and Blender.

Ok, Ubuntu installer wants an internet connection, so I'll see you on the other side.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### Gimp works for me. A good price, too.(4+ / 0-)
Recommended by:
Orinoco, palantir, jessical, Larsstephens

Peace ☮ Health ♡ Happy New Year

[ Parent ]

• ##### Gimp is free(3+ / 0-)
Recommended by:
palantir, jessical, Larsstephens

The Wacom Intuos pen tablet to go with it was \$200. lol.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### What I really like about this diary(1+ / 0-)
Recommended by:
Larsstephens

is that it spites all the dumbass countries out there that use the metric system!

By the time they get the milk converted from liters to gallons, I'll already have my graph completely plotted!

• ##### We are converting the milk (4+ / 0-)

to cheese, not liters. Goat cheese. Fromage de chèvre.

Good stuff.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### Off Topic(3+ / 0-)
Recommended by:
Orinoco, jessical, Larsstephens

When I see 32, I think that is the best double out in darts!

• ##### funny, I see 100,000 :} n/t(1+ / 0-)
Recommended by:
Larsstephens

...j'ai découvert que tout le malheur des hommes vient d'une seule chose, qui est de ne savoir pas demeurer en repos dans une chambre.

[ Parent ]

• ##### There are 10 kinds of people in the world(2+ / 0-)
Recommended by:
jessical, Pale Jenova

Those who know binary, and those who don't. :)

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

#### Permalink

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