Question

A telephone company offers two plans with per-minute charges. Plan A involves a monthly rental of $12, and call charges at 7¢ per minute. Plan B involves a monthly rental of $15, and call charges at 5¢ per minute.


Write an inequality in terms of the number of minutes which shows when Plan A is less expensive than Plan B. Solve the inequality, showing the

Answer 1

somebody please help omg I will do anything!!! im so stuck on this!:(

Answer 2

its supposed to say, "solve the inequality showing the steps in your work."

Answer 3

can you write an equation for the cost on plan A if \(m\) is the number of minutes used? how about for plan B?

Answer 4

@LGumboymath234

Answer 5

yes I just have to write an inequality that includes both plans but it has to show how plan A is less expensive @whpalmer4

Answer 6

and I am trying to lead you through it. Do you know how to write the equations or expressions I requested? If so, would you do so, please?

Answer 7

no I don't know how! all I have to do is write it and solve it and im having trouble with both

Answer 8

@whpalmer4 do you not know how?

Answer 9

I most certainly do know how. But I can't help you if you don't take part.

Read the problem. Can you tell me how to find the cost under plan A if I spend \(m\) minutes using the phone in a month?

Answer 10

add the amount of minutes to the plan price?

Answer 11

Plan A involves a monthly rental of $12 plus call charges at 7 cents/minute.

Answer 12

yes

Answer 13

can you write an algebraic expression that expresses that cost in dollars?

Answer 14

y=7x+12??

Answer 15

close. how many dollars is 7 cents?

Answer 16

.7 haha

Answer 17

are you sure about that?

Answer 18

I'm pretty sure a dollar is 100 cents, so 1 cent is 1/100 dollars, or $0.01
and then 7 cents would be 7*$0.01 = $0.07

Answer 19

ohh yea. sorry I was trying to type that and send it but connexus shut down

Answer 20

ok, so plan A cost is monthly rental plus minutes charges or
\[A = 12+0.07m\]where \(m\) is number of minutes used, and the costs is in dollars

Answer 21

okay

Answer 22

now we have to do the same for B

Plan B involves a monthly rental of $15, and call charges at 5¢ per minute.

Answer 23

so A=15+0.05m

Answer 24

well, \[B = 15+0.05m\]

now we want to write the inequality for A being less expensive than B

\[A<B\]\[12+0.07m<15+0.05m\]

Answer 25

now you just need to reduce that down so \(m\) is alone and there's a number on the other side of the inequality sign

Answer 26

this works just like solving in an equation, except if you multiply or divide by a negative number, you must reverse the inequality sign

Answer 27

so would I subtract .05 from .07?

Answer 28

no, start with the plain numbers (not multiplying any variables) first

Answer 29

so subtract 12 from 15?

Answer 30

subtract 12 from both sides

Answer 31

you do the same thing to each side

Answer 32

okay I have 0.07m<3+0.05m

Answer 33

now I would get rid of the decimals by multiplying each side by 100

Answer 34

how would I write that?? sorry ive never done this before

Answer 35

\[100*0.07m<100*3+100*0.05m\]
\[7m < 300 + 5m\]

Answer 36

okay thank you so much! so would I subtract 5 from 7

Answer 37

no, subtract \(5m\) from both sides

Answer 38

yea sorry that's what I mean haha!

Answer 39

so do I divide both sides by 2 now?

Answer 40

yes

Answer 41

so I got m<150 should my sign be reversed? or would it stay like that since it was reversed when multiplying and then reversed back when I divided?

Answer 42

we never multiplied or divided by a negative number, so the sign keeps the original orientation

Answer 43

ohhh okay thank you sooo much!! do you mind helping me with one more! its very simple I just don't get it! this will be the last question I promise haha

Answer 44

so when is it cheaper to use plan A? how about plan B

Answer 45

plan a is always cheaper right? or do we now have to work out plan b because I thought we just did both

Answer 46

no, plan A is cheaper only when you use fewer than 150 minutes, assuming you ended up with \[m<150\]

at exactly 150 minutes, they both cost the same.

at more than 150 minutes, plan B is cheaper.

think of it this way - with plan B, you pay an extra $3 per month to save 2 cents per minute (= 41 for 50 minutes). after 150 minutes, the per-minute savings is larger than the additional up-front cost, so if you talk a lot (more than 150 minutes) plan B is cheaper

Answer 47

when we wrote the inequality, we chose which condition we were looking for by our choice of inequality (or equality) sign

\[A<B\]finds values of \(m\) where plan A costs less
\[A=B\]finds value where both plans are equal in cost
\[A>B\]finds values of \*m\) where plan B costs less

of course, you can figure out the other two from which ever one you chose easily enough in this case

Answer 48

sorry, fat-fingered the formatting on the last one, should be "finds values of \(m\) where plan B costs less"

Answer 49

does that make sense? this is why I asked you to write the expression for each part separately, so you could see how we could fit them together to answer any of the potential questions

Answer 50

ohhhhhh okay that makes so much more sence now. I do online school and its so hard to learn mth from my teachers so thank you!

Answer 51

so do you think you could help on just one more question?

Answer 52

sure, but I can't spend as long on it

Answer 53

okay that's fine,

ace $55 $0.05
blaster $30 $0.03


these are car rental companys. the first number is the flat fee and the second one is the cost per mile

Answer 54

I have to write a linear equation for both and solve them separately and I tried but I got confused

Answer 55

ok, same setup as with the phone plans

Answer 56

but are you sure you have the numbers right? here, blaster is always cheaper with the numbers you provided

Answer 57

0.08 I mean!

Answer 58

so would it be y=0.05x+55
and y=0.08x+30 ???

Answer 59

Sorry, had to go out for a few hours, didn't mean to leave you hanging!

Yes, those equations appear correct. Set the parts containing \(x\) equal to each other and solve for \(x\) to find the number of miles where they cost the same. Or set it up as an inequality to see which one is cheaper for a given distance.