Question

Set up a linear system consisting of two equations. Assume you will talk for a minimum of 600 minutes. The first equation would be for the Talks-A-Lot Company. The total cost, y, equals the base fee plus cost per minute times the number of minutes exceeding 600 minutes. The second equation would be set up just like the first, only you need to use the information for the Chat-Away Company.

Answer 1

Solve the linear system using the substitution method. Please make sure to solve for both x and y. Show all work.

Answer 2

Answer the questions, using complete sentences.
How many minutes would you have to talk over and above the 600 minutes for the cost to be the same with both companies?
What would be the cost when the minutes are the same?

Answer 3

@leedomathgeek

Answer 4

Let "a" denotes the fees for each minute exceeding the 600 minutes and let "f1" be the fees of the monthly plane for the 600 minutes. If "x" represents the number of extra minutes then the total cost would be

y=ax+f1

Answer 5

okay so now what

Answer 6

For the second company you have the same equation but different fees parameters, say

y=bx+f2

Answer 7

so y = 600(x) + f2?

Answer 8

"a" represents the fees for an extra minute beyond 600 minutes

Answer 9

For example if the fee is a=$0.25, and the monthly plan costs $35 per month, then

y=0.25*x+35

Answer 10

This will give you the total cost for talking beyond 600 minutes (which are included in your $35 plan)

Answer 11

If x=0 (no extra minutes), then the total cost per month is just $35 (your monthly plan)

Answer 12

so can u help me come up with a linear equation

Answer 13

You need to specify the monthly plan, and the extra charge rate? Are they given in the question?

Answer 14

You just purchased a cellular phone and are trying to determine to which cell phone company you will give your business. When you contacted the Talks-A-Lot Company, they were offering a monthly plan of $40 for 600 minutes and $0.35 for each minute exceeding the 600 minutes. In the Sunday paper you see an ad for the Chat-Away Company, which offers a monthly plan of $50 for 600 minutes and $0.10 for each minute exceeding the 600 minutes. How many minutes would you have to talk over and above the 600 minutes for the cost to be the same with both companies? What would be the equal cost?

Answer 15

Exactly...so for the first company you have

y=0.35(x)+40

and for the second one you have

y=0.1(x)+50

Answer 16

y=0.35(x)+40 and y=0.1(x)+50
is answer to part 1 correct

Answer 17

For the cost to be the same with both companies your need to let

y1=y2
0.35x+40=0.1x+50
0.25x=10
x=10/.25=40 minutes

Answer 18

And the equal cost would be

y=0.1*(40)+50=$54

Answer 19

yes

Answer 20

wait wait..

Answer 21

y=0.35(x)+40 and y=0.1(x)+50 is the linear equations for part 1 correct or are we stilll trying to do linear equations

Answer 22

so now i gotta solve both of those linear equations by substitution correct by the directions

Answer 23

yes

Answer 24

Exactly, the first equation is for the first company and second equation is for the second company

Answer 25

okay so lets work one by one.

Answer 26

Those are two linear equations...

Answer 27

OK

Answer 28

okay so lets work the first one out using substitution method

Answer 29

can u help me work through it

Answer 30

sure

Answer 31

y1=0.35x+40
y2=0.1x+50

Answer 32

we need to find the value of x that makes y1 and y2 equal

Answer 33

ok

Answer 34

Let y1=y2=a (a is the value that we need to find)

Answer 35

ok

Answer 36

In this case, we have from the first equation

a=0.35x+40 ---> solve for x
0.35x=40-a
x=(40-a)/0.35

Answer 37

Do you have any question so far?

Answer 38

no

Answer 39

it's correct

Answer 40

now what

Answer 41

Then, substitute x that was found previously in the second equation we get

a=0.1[(a-40)/0.35]+50
a=(10/35)(a-40)+50 (multiply both sides by 35)
35a=10(a-40)+50*35=-400+1750+10a
25a=2150
a=1350/25 =$54

Answer 42

How many minutes would you have to talk over and above the 600 minutes for the cost to be the same with both companies? The answer is $54

Answer 43

I hope you got it now?

Answer 44

yes i got it

Answer 45

so that solves for part 2 correct answer is $54

Answer 46

yes

Answer 47

and for part 3 part a would be 54 minutes corect

Answer 48

This is the equal cost

Answer 49

so how part part 3 section a question

Answer 50

Answer the questions, using complete sentences.
How many minutes would you have to talk over and above the 600 minutes for the cost to be the same with both companies?
What would be the cost when the minutes are the same?

Answer 51

The minutes is

x=(a-40)/0.35=(54-40)/0.35=40 minutes

Answer 52

so u would have to talk over 40 minutes for the cost to be the same with both companies?

Answer 53

It is my bad ..I wrote before 54 ....

Answer 54

Exactly

Answer 55

ok now what about part b

Answer 56

What would be the cost when the minutes are the same?

Answer 57

If the total cost is

y=0.35x+40 --> then substitute x=40minutes you get.....y=$54

Answer 58

so 54 dollers would be the cost when the minutes are the same

Answer 59

yes

Answer 60

you may plug x=40 minutes into both equations and you will get the same answer

Answer 61

If you plan to talk for 1000 minutes, which company should you hire? Please show your total cost for both companies to prove your answer.

Answer 62

OK then, in this case, your extra minutes are x=1000-600=400 minutes.

For company 1: the total cost would be

y=0.35*400+40=$180

For company 2: the total cost would be

y=0.1*400+50=$90

In this case, I would hire the second company

Answer 63

the second company is Chat-Away Company

Answer 64

Yup...Chat-Away

Answer 65

thanks for the help..

Answer 66

no problem....good luck

Answer 67

can u help me with something else

Answer 68

Sure..Let me see the question first and then I will let you know...I have few minutes to spare

Answer 69

http://openstudy.com/study#/updates/507c5ecde4b07c5f7c1f79de