Question

Company A rents copiers for a monthly charge of $300 plus 12 cents per copy. Company B rents copiers for a monthly charge of $600 plus 6 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

Answer 1

any takers

Answer 2

can someone help me

Answer 3

How far have you gotten on this?

Answer 4

Not too far

Answer 5

Well, show me where you're at and let's see if we can't get an answer.

Answer 6

I have another question that needs to be answered besides that one

Answer 7

We should probably do one at a time.

Answer 8

Yea but I'm doing online courses that need to be completed before the end of July and now I have a geometry question

Answer 9

Let's see how far you've gotten on this one.

Answer 10

Well I didn't get far at all on it

Answer 11

That's okay, show me what you have done.

Answer 12

The only thing I've done is stare at the question that's why I'm here

Answer 13

I'm not the best at any kind of math besides counting and multiplication

Answer 14

You might just surprise yourself. Okay, so this appears to be an inequality equation so why don't we start by writing what we know. Put what you know about the cost under the labels:

Company A Company B

Answer 15

well company A is 300 dollars and company B is 600 dollars

Answer 16

Those are the initial costs, what about the cost per page?

Answer 17

ah I think 12 and 6

Answer 18

cents

Answer 19

Yes, but we need this in similar units AND we need it in the form of an expression of cost.

Answer 20

That's where I'm lost

Answer 21

So we would want to write something like:
Company A Company B
$300 + $0.12 $600 + $0.06

Answer 22

should I take notes

Answer 23

Now what does the question want you to find out?

Answer 24

You could refer back to this, remember it, or take notes to refer to, it is really up to you.

Answer 25

That's what I'm doing. Now the problem wants me to find company A's charges compared to B's and see if it is higher

Answer 26

True, but more specifically they are saying, if you made an equal amount of copies at both businesses, how many copies would you need to make before company A costs you more money?

Answer 27

Yea that's right but how

Answer 28

If you made 2 copies at both places, how much would you spend at each?

Answer 29

300 and 600?

Answer 30

Did both places give you 2 free copies?

Answer 31

no

Answer 32

Okay, so how much would it cost you?

Answer 33

Uhh don't you have to multiply or divide

Answer 34

Yes, you do have to do one of those. :)
Think about what it is telling you, because if you don't understand what information it is giving you then it will make solving this much more difficult.
Company A says that they will charge you $300 plus $0.12 for each copy.

Answer 35

And right now you want 2 copies.

Answer 36

Yea

Answer 37

so what should I do first

Answer 38

How would you determine the total cost to make 2 copies, without counting the rental fee?

Answer 39

divide

Answer 40

Alright, divide what?

Answer 41

the monthly charge with the cents per copy

Answer 42

How are the two charges related? Does the monthly charge change if I make one copy or twenty copies?

Answer 43

No it doesn't because it's the starting charge... I think

Answer 44

Exactly. The only thing that will change how much I will pay is the number of copies I actually make.

Answer 45

Ok so what I need to do is take 300/12 and 600/6 and I'll get my answer?

Answer 46

Why are you dividing the rental fee again? If you are renting copiers from me, I am going to take that 300 dollars and put it in my pocket, PLUS $0.12 PER copy that you make. So if you make 0 copies, I get $300, if you make 1 copy, I get $300.12.

Answer 47

Aw ok I see where that happens so all I do multiply or add it seems to me like I add

Answer 48

Write out the equation to calculate the total charge for 5 copies then.

Answer 49

So we have 0 copies= 300, 1 copy= 300.12, 2 copies=300.24 am I right so far

Answer 50

Yes you are. Can you write an expression to represent what you're doing? What if you had to calculate 1000 copies.

Answer 51

I know that 1000 is x so we need to find y but I get confused when I have to find it because I don't know all the steps

Answer 52

or is1000 the y

Answer 53

There is no 'y' in this problem. We will be using 'x', but not just yet.

Answer 54

ok when

Answer 55

If you can visualize there being a variable here then you should be able to write an expression like we did earlier, only with the added information for the operation on the copies you were just doing.

Answer 56

I can't visualize it well I can I just don't know if I'm doing it right

Answer 57

Write it out and I will tell you if you are.

Answer 58

Hmm so would it be 12+300x=1000

Answer 59

You have it multiplying your rental fee, why wouldn't you multiply your copy charge?

Answer 60

I got confused

Answer 61

so it would be 300+12x=1000

Answer 62

The 1000, in this example, is what you would put in place of your 'x'. You would have to calculate the equation to get what it equals.

Answer 63

Ok so 1000 is the x no y value so now what I do is find what equals the x

Answer 64

In this example the 1000 IS your 'x'. So you do not need to see how much it is.

Answer 65

right ok man this is confusing

Answer 66

If you went to a carnival and played the game where you throw balls at the plates, and the guy says that you get 3 balls for a dollar.
How much would it cost you to throw 3 balls?

Answer 67

a dollar

Answer 68

is that right

Answer 69

Yes it is. What if you wanted to throw 6 balls?

Answer 70

18 right

Answer 71

cause 3x6=18

Answer 72

Sorry, my system became unstable... And no, you get 3 for $1, so for every $1 you are handed 3 balls.
Now, if you wanted to throw 6 balls, how much would it cost?

Answer 73

it would be 2 dollars

Answer 74

Right, now you can think about the 3 balls as a "set". So you get 1 "set" for 1 dollar, you get 2 "sets" (6 balls) for 2 dollars, what if you wanted to throw 3 "sets"?

Answer 75

9 dollars

Answer 76

If you get 1 set for a dollar, how much is 3 sets?

Answer 77

aw apologies 3dollars

Answer 78

Exactly

Answer 79

So how are you getting the cost? What if I asked you how much it would be to throw 10 sets?

Answer 80

so 30

Answer 81

If you get 1set for $1, 10 sets is ?

Answer 82

I feel I need to point out that if you are having difficulty with this concept, the geometry you referenced earlier will be very difficult.

Answer 83

Yes it is

Answer 84

I'm trying to count by 3 but I guess that's wrong

Answer 85

You need to count by the number it costs you each time. You only care about what is changing, each set you get will always have 3 balls. However you are changing the number of sets you get, which has a charge associated with each.

Answer 86

If I punch you in the arm twice, each time you flinch, and you flinch three times, I get to punch you twice for each one, so 2(punches) multiplied by 3(flinches) means that I get to punch you 6 times.

Answer 87

If I am going to give you 7 cents every time I step on a crack in the side walk, the amount I pay for each crack doesn't change, the number of cracks I step on does.
So if I were to step on 0 cracks, you get 7cents times 0, if I stepped on 12 cracks, you get 7 cents times 12.

Answer 88

aw that makes sense

Answer 89

Well let's see if it does.. :)
If I charge you 12 cents for every copy you make, how much will it cost you to make 4 copies?

Answer 90

Think about what is changing and what stays the same.

Answer 91

is it 48 dollars

Answer 92

or 12+4=18 dollars

Answer 93

Well your first answer was basically correct, although it is cents and not dollars.
Your second answer is not right in any way.

Answer 94

ok so its 48 cents got it

Answer 95

Now how did you get that?

Answer 96

I multiplied 12 times 4

Answer 97

Excellent, that is great. Okay, so what if you made 6 copies?

Answer 98

is it 72