Question

Please help!

A cell phone company offers you a plan that charges a flat rate of $25 per month for 200 minutes of airtime. The rate of any time in excess of 200 minutes is $.12 per minute.

A. Write an expression for the monthly dollar amount spent for the cell phone service if you want use x minutes of airtime in excess of 200 minutes.

B. Write an inequality which indicates that you have budgeted no more than $40 per month to spend on the service.

C. Determine the maximum number of minutes you can use in excess of 200 minutes so that you do not exceed your $40 per month budget.

Answer 1

part A)

we are told that "you want use x minutes of airtime in excess of 200 minutes", so automatically we know that x > 200

The company charges $25 per month for those 200 minutes. So that base charge of $25 is always there. Because x > 200, we're going to be charged $0.12 per minute on top of this $25

The remaining time over 200 minutes is x - 200. So 0.12(x-200) is added onto 25 to get


25 + 0.12(x-200)


which is the total amount spent if x > 200 (ie you use more than 200 minutes)

Answer 2

how would we do part B?

Answer 3

Do we just double the equation?

Answer 4

Wait no I don't think we do that.

Answer 5

we need to write an inequality

Answer 6

if T is the total cost, if we budget $40 for that total cost, then

T <= 40

25 + 0.12(x-200) <= 40

Answer 7

Notice how

a) the total cost T is less than or equal to $40

and

b) the total cost is also equal to 25 + 0.12(x-200)

Answer 8

for part C, you need to solve the inequality found in part B

Answer 9

So the answer would be 49 maximum number of minutes you can use in excess of 200 minutes so that you do not exceed your $40 per month budget?

Answer 10

25 + 0.12(x-200) <= 40

25 + 0.12x-0.12*200 <= 40

25 + 0.12x-24 <= 40

0.12x+1 <= 40

0.12x <= 40-1

0.12x <= 39

x <= 39/0.12

x <= 325

So you can talk a max of 325 minutes to stay within budget of $40

Answer 11

No you're not. You just need more practice.

Answer 12

I haven't learned any of this and my teacher expect my classmates and I to do this at home.

Answer 13

which part isn't making sense?

Answer 14

I understand the equation part but when we have to solve the inequality is where I get lost.

Answer 15

are you familiar with solving equations?

Answer 16

Not really

Answer 17

if you have something like x+5 = 10, then how do we isolate x?

Answer 18

You subtract it from each side?

Answer 19

yes, you undo the +5 and subtract it from both sides

Answer 20

the same idea applies to 0.12x+1 <= 40

we undo the +1 by subtracting 1 from both sides

Answer 21

Then whats the point of adding it there lol

Answer 22

then we undo the 0.12 times x by dividing both sides by 0.12

to go from

0.12x <= 39

to

x <= 39/0.12

Answer 23

because the original equation allows you to find the total cost for any x

Answer 24

Ohhhhh I understand.

Answer 25

So then 39/0.12 gives us 325!

Answer 26

and when you set that total cost equal to 40 and solve, you are essentially forcing the total cost to be $40 and then finding the x value that makes the total cost equal to 40

Answer 27

exactly

Answer 28

Oh thank you so much it's more clear to understand now.

Answer 29

I'm glad it is