Question

Who can help me with this word problem. representing and solving it with using a graph, table and algebra?

Answer 1

You want to join a health club for one year. Club A charges $55 per month and has no initiation fee. Club B costs $45 a month and has an initiation fee of $100. At what month are the costs of the two clubs the same?

Answer 2

@563blackghost

Answer 3

@dude

Answer 4

Lets make an equation for Club A first
A line is written as \(y=mx+b\)

m is the rate, and b is the initial point

Based on this can you make the equation for Club A?

Answer 5

y = 55x umm

Answer 6

Right

Answer 7

oh alright

Answer 8

`Club B costs $45 a month and has an initiation fee of $100`

Now we do the same thing for Club B
____________________________________________________

\(y=mx+b\)
A line is written as y=mx+b

m is the rate, and b is the initial point
____________________________________________________

Answer 9

would u say the intuition fee is the initial point?

Answer 10

Realized I copy pasted that incorrectly but it will have to do.

Answer 11

Yes

Answer 12

y = 45x + 100

Answer 13

Looks good

Answer 14

Now is asks when they will be the same


Another word for same is equal aka =

Set them equal to each other

Answer 15

55x = 45x + 100

Answer 16

Right, not get x on one side of the equation

Answer 17

55x = 45x + 100
/45 /45 /45

Answer 18

1.2x = 2.2 ?

Answer 19

Not quite, opposite of +45x is subtracting 45x on both sides

Answer 20

OH

Answer 21

55x = 45x + 100
-45 -45 -45
10X = 55

Answer 22

You're subtracting 45x on both sides, 100 and 45x are not like terms so you cannot subtract them

\(~~~~55x = 45x + 100\\
-45x ~-45x \\
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\
~~~10x = 100\)

Answer 23

Oh, so only from the X's not all of them

Answer 24

someone told me all of them woopsie daisy

Answer 25

someone told me all of them woopsie daisy

Answer 26

10x =100
/10 /10

Answer 27

Yes

Answer 28

x = 10

Answer 29

Right

x = months

So after 10 months, they will have the same cost

Answer 30

oooooo

Answer 31

oooooo

Answer 32

so now i have to do this on a graph

Answer 33

You could use technology for this but are you graphing this manually?

Answer 34

i could use desmos, do i just apply the two formulas?

Answer 35

Yeah
\(y=55x\)
and
\( y= 45x + 100\)

Answer 36

alright ill do that rn, in then lastly its doing a table

Answer 37

You can use the graph to find the points, just write x=1, x=2 and x=3

Where they intersect is the point

Answer 38

wait i did it wrong i think where did u get those numbers

Answer 39

That is right, the window is just out of place because you're only looking at single digits xD

Answer 40

oH but how do i find the points if they look like this

Answer 41

https://www.desmos.com/calculator/j7xlduk0me

Answer 42

Yeh

Answer 43

what do i do wit the 550

Answer 44

That is just the cost, when they are both at 10 months

Answer 45

ooHHHHHHHHHHHHHHhhhh

Answer 46

ok now for the table :D:D:D:D:D:D

Answer 47

lmao

Answer 48

ill make the table n see if it looks right

Answer 49

Okay

Answer 50

hows this

Answer 51

should prob make the left part longer cuz its months?

Answer 52

Dude, every x value is a month, you only need 2 rows xD

Answer 53

wdf

Answer 54

ok ignore the left part

Answer 55

:3

Answer 56

It was right, rows are the horizontal xD

You dont need many of the horizontal unless it was given to you like that

Answer 57

i thought i would make 10 slots for 10 months yknow

Answer 58

You can do that

Answer 59

Unless it specified, its up to you

Answer 60

ill do it if it works

Answer 61

so for the cost of club a, it doesnt have a rising point

Answer 62

Rising point?

Answer 63

OH I MEANT initial point

Answer 64

Yes, that starts at 0

Answer 65

so they both start at 0 on day 0?

Answer 66

No, just Club A starts at 0

Answer 67

Yes, the months for that would be 0

Answer 68

so the months start at 0 too?

Answer 69

Yeah because at 0 months, the cost is 0 for Club A

Answer 70

and club B starts with 100?

Answer 71

Yes

Answer 72

Right

Answer 73

ill do the club b rq

Answer 74

Looks good :P

Answer 75

so do i start club a with 55?

Answer 76

Month 1 is 55, yes

Answer 77

and i add 55 each time?

Answer 78

Yes

Answer 79

okie

Answer 80

BAM

Answer 81

Perfect

Answer 82

yayy thankssss

Answer 83

Ofcs