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@ilyalgebra
I was just checking and this happen. Google ships PruCan.
prucan, spamano, and fruk GO
And everything turned out wonderfully in the end
Prussia and Fem!Canada's Wedding
Canada’s Dress:
The Ceremony:
First Dance: By My Side
Du bist mein Ein und Alles (You mean the world to me)
My heart belongs to you~
Du bist mein Ein und Alles Is You are my one and only in German.....
I (again) used my solution from before
(You will not gain or lose money if you
sell 40 batches) and I thought that if
you sell 39 or less batches, you will
lose money.
Start with the equations from the
first problem
6x+30=y
.5x+250=y
Then substitute 39 for "x"
6(39)+30=y
.5(39)+250=y
Which is equivalent to
234+30=y
19.50+250=y
You will subtract 264 from 269.50 to get 5.50.
You will owe 5.50 if you sell 39 batches so
if you sell even less than that, you will ow more.
~Mey-Rin, Bea, and Pandy
In the previous problem, I stated that you
will not earn or lose money if you sell 4
batches.Well if you don't gain or lose at
40 but you want to earn you have to sell
more and selling 41 batches earns you
a profit of $5.50.
If you take the equations from the first
problem
6x+30=y
.5x+250=y
Then you substitute 41 for "X"
6(41)+30=y
.5(41)+250=y
Which is equivalent to
246+30=y
20.50+250=y
And then you're left with
276-270.50=5.50
Which is your profit. So the
more batches you make, the more money
you'll earn.
~Mey-Rin, Bea, and Pandy
You will start with your 2 equations
from problem 1
6x+30=y
.5x+250=y
The 40 batches will be the "X"
value (Independent variable)
6(40)+30=y
.5(40)+250=y
Which is equivalent to:
240+30=y
20+250=y
Both of those equations equal 270 and
subtracting a number by itself gives you
zero so your profit is zero and you do
not owe any money
~Mey-Rin, Bea, and Pandy
Just explaining question 4
~Mey-Rin, Bea, and Pandy
This one will be very simple to explain but is easy
to get lost in so please pay attention. You will
type in your solutions and coefficients:
6 30 1
.5 250 1
After you use a calculator to generate this,
you will get this matrix:
1 0 40
0 1 270
Now, it looks hard to comprehend, but it really isn't.
1 0 40
Is how many batches were sold on a day
0 1 270
Is how much it has cost them
~Mey-Rin, Bea, and Pandy
Start with these 2 equations:
6x+30=y
.5x+250=y
You will multiply .5x by -12 to get -6x
6x+30=y
-6x+250=y
You will also multiply 250 and y by -12
6x+30=y
-6x-3000=-12y
First you will add 6x to -6x to get:
30=y
-3000=-12y
Then, you will add 30 to -3000 to get: (don't forget
to add 1y to -12y to get -11y!!)
-11y= -2970
Finally, you will divide -2970 by -11y to get:
y=270
As you do in substitution, you will substitute 270 in
one of the problems like this:
270=6x+30
Then you will subtract 30 from 270 to get:
240=6x
Finally, you will divide 240 by 6x to get:
x=40
Our variables have been defined as:
Batches sold(40): x
Cost ($270): y
~Mey-Rin, Bea, and Pandy
To start, you will need to have these 2 equations:
6x+30=y
.5x+250=y
In substitution, you have to solve for the variables so
then you will get this equation:
6x+30=.5x+250
You got this since both equations were equivalent to "Y".
You subtract .5x from 6x to be left with 5.5x:
5.5x+30=250
Then, you'll subtract 30 from 250 to be left with 220.
5.5x=220
You'll divide 220 by 5.5 to get 40
x=40
If you substitute the 40 into one of the equations,
6x+30=y
6 mutiplied by 40 is 240
6x40=240
If you add 30 to that you should get 270
240+30=270
y=270
We previously defined the variables as:
X: batches sold (40)
Y: Money spent ($270)
~Mey-Rin, Bea, and Pandy
Sometimes you have to solve a system by graphing which is okay,
but not always ideal. We had a Y-Intercept of 250 on one of the
equations! This would not have been fun to do on paper so we
solved it using this program:
Desmos Graphing Calculator
So you have to type your first equation on the left box labeled
"1". Then you click the box under that labeled "2" and type
the final equation. The solution is where the lines intersect so
at point (40,270) these two lines intersect leaving it to be the
solution. But what does (40,270) mean? It's this simple:
X axis=Batches sold
Y axis= Money that was paid
40=X
270=Y
40 batches of cupcakes were sold
$270=amount paid
~Mey-Rin, Bea, and Pandy
Problem 1
(All credit to Mr.Horn. He's great!)
So in the income part, it states that we are earning $6 for every
cupcake batch sold, and that you will earn an additional
$30 since you're allowing the local theatre to advertise on
your window. We have been taught to put our equations in
slope-intercept form:
y=mx+b
~or~
Solution=Slope(independent variable)+y-intercept
Since we don't know our solution we shall leave it as "y".
The slope would be the $6 since it's the rate of change(m),
and $30 will be our y-intercept (b) since it is our "starting value".
So the equation looks like this:
y=6x+30
This problem also requires us to find the costs of our company.
Again, we will be using slope-intercept form; (if you do not remember
what it is, please see the information on the right of the grey line.)
so information says that to run electricity and pay your employees,
you will have to pay $250 every day; and you pay $.50 for every batch
since you have to (obviously) pay for the ingredients. So you don't
know the solution yet, so it will remain "y". You know you will pay
$250 for paying your employees and running electricity everyday
which would be the y-intercept (b) , and you know that you will pay
$.50(m) for the ingredients used per batch. Now, I know that you
might be thinking something along the lines of this:
"Why would the $250 payment be your y-intercept if
it's being paid per day?"
That is something I thought at first as well. You know that you will
pay $250 per day of work but, you do not know how many batches
of cupcakes will be produced per day making $.50 the slope(m) since
it has close relations to the independent variable. This equation,
will look like this:
y=.50x+250
So to recap on what I just did, (by that, I mean here's the answers):
Income is: y=6x+30
Cost is: y=.50x+250
Thanks for reading and come back for more!
~Mey-Rin, Bea, and Pandy