Question

Fan and Medal!!


The area of a rectangular piece of land is 240 square meters.
If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square.

Part A: Write an equation to find the width (x) of the land. Show the steps of your work.

Part B: What is the width of the land in meters? Show the steps of your work.

Answer 1

A square would be X by X

This rectangle is said to be (X-5) by (X+3)

Answer 2

(X-5)(X+3) = 240

Answer 3

(x+3)(x-5)=240?

Answer 4

Okay I got that

Answer 5

yes

Answer 6

What do I do now?

Answer 7

do you know how to find the area of a rectangle

Answer 8

Solve for X, you will get 2 answers, the positive one is correct

Answer 9

do I FOIL (x+3)(x-5)?

Answer 10

yes

Answer 11

I ended up getting x^2-2x-15

Answer 12

move the 240 over now to get

x^2 - 2x - 255 = 0

Answer 13

factor that, or use the quadratic formula , since it is a book prob, it will probably factor nice

Answer 14

Do I make that into two binomials?

Answer 15

yep

(x-17)(x+15)=0

Answer 16

Wait how did you get the 17 and 15?

Answer 17

255 = 17 * 15
and
15 - 17 = -2 (middle number)

Answer 18

If you multiply that out, you get back to the original ax^2 + bx + c = 0

Answer 19

Ohhh okay I understand that

Answer 20

or you could always just apply the quadratic formula, and you would get the X values

Answer 21

so now you have
(x-17)(x+15)=0

which means either term can be zero, so

(x-17)=0 or (x+15)=0

X=17 or X=-15

Answer 22

The problem is a physical measure, so the positive value is the one that makes sense...

X=17

Answer 23

What do I write for part A and for Part B?

Answer 24

First Part...

Area of Land = Length * Width = 240

240 = (X-5)(X+3)

Answer 25

And do I work it out until I get (x-17)(x+15) = 0?

Answer 26

right, for the second part you solve it

Answer 27

Thank you sososo much! You really helped a lot.

Answer 28

yw

Answer 29

Do you think you can check over some of my answers? If you have the time of course

Answer 30

sure

Answer 31

Thanks so much!
They're quite long, so do you want me to screenshot it and attach it?

Answer 32

Sure, i have a bit of time

Answer 33

And that's it, since I don't want to have you check all of them, haha

Answer 34

The first one looks good, what is the prob with that one?

Answer 35

I just wanted to see if I got it correct or not

Answer 36

That one looks good to me

Answer 37

Thank you (:

Answer 38

second one looks good too

Answer 39

yay ^-^

Answer 40

For the last one part C, it asks if they all have a common factor

Answer 41

Yes, is it wrong?

Answer 42

I don't see a common factor btw all 3 of those

Answer 43

So it would be no because no common factor is consistent between the three polynomials?

Answer 44

yeah i think so

Answer 45

Do you think you could check 2 more?

Answer 46

k, real quick, then i have to go... you can fan me for help later if you want

Answer 47

Alright! Once I finish with these questions, I'll be done with Algebra for the year, aha

Answer 48

haha

Answer 49

And that's it!

Answer 50

For the first, for the domain, be sure to call the variable 't' and not x, Since y is a function of t, in S(t)

Answer 51

Okay

Answer 52

anything else?

Answer 53

nope, looks good to me

Answer 54

Yay!

Answer 55

Did you check the last one? or

Answer 56

Part b asks what the maximum profit is, you dont say what that is

Answer 57

How do I find the maximum?

Answer 58

it would be at the vertex of the parabola, or axis of symmetry value

Answer 59

How do I find that? Did my steps correspond to the question at all?

Answer 60

It looks like you have P(n) written in vertex form in part b right... so you can use that to extract the vertex coordinate (h,k)

Answer 61

Huh?

Answer 62

vertex point - (h,k)

Vertex Equation - y = a(x-h)^2+k

Answer 63

Do I need to rewrite anything?

Answer 64

so the vertex from your equation is at the point, (5, 2250)

Answer 65

This is so confusing ._. I'm sorry that I'm so difficult to work with

Answer 66

sorry i said year... the most profit is at (5,2250) price 5 and prfit 2250

Answer 67

How do I find that with the steps I wrote down?

Answer 68

which is also on the axis of symmetry

Answer 69

The last thing you wrote, is the vertex equation for the parabola.

vertex point - (h,k)
Vertex Equation - y = a(x-h)^2+k

The maximum profit 'k' is at that vertex point, you can just read it from your equation.

Answer 70

Ahhh okay! So now I write that the maximum profit is 2250 ?

Answer 71

yes, The vertex is at point (5,2250)

When the tickets are sold at 5 dollars each, the profit is the most at 2250 dollars.

Answer 72

Thank you sosososo much!! You're truly a lifesaver, I wish I could give you a thousand medals , haha