Ich liebe algebra

Hallo! We're a non-helper blog so please refrain from leaving an ask in or ask box, please! ~Mey-Rin, Bea, and Pandy

[chiibitalia-deactivated20170207]

I was just checking and this happen. Google ships PruCan.

[btt-texts]

prucan, spamano, and fruk GO

And everything turned out wonderfully in the end

[the-little-wedding-planner]

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~

[ilyalgebra]

Du bist mein Ein und Alles Is You are my one and only in German.....

[ilyalgebra]

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

[ilyalgebra]

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

[ilyalgebra]

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

[ilyalgebra]

Just explaining question 4

~Mey-Rin, Bea, and Pandy

[ilyalgebra]

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

[ilyalgebra]

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

[ilyalgebra]

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

[ilyalgebra]

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

[ilyalgebra]

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