Write an inequality that represents the following problem. There are two cell phone plans available from Cell Phones R Us company. Plan A charges $30 a month plus $0.01 for every text message. Plan B charges $20 a month plus $0.05 for every text message. How many text messages do you need to send in order for Plan A to be cheaper than Plan B?

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cellyp4sc cellyp4sc

07-10-2016
Mathematics

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Write an inequality that represents the following problem. There are two cell phone plans available from Cell Phones R Us company. Plan A charges $30 a month plus $0.01 for every text message. Plan B charges $20 a month plus $0.05 for every text message. How many text messages do you need to send in order for Plan A to be cheaper than Plan B?

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Hussain514 Hussain514 · Answer 1 · 2016-10-20T11:04:02+02:00

Hussain514 Hussain514

20-10-2016

if PLAN A is cheaper than PLAN B then,
P (A) < P (B)
30+0.01t < 20+0.05t (subtract 0.05t from both sides)
29.95-0.04t < 19.95 (subtract 29.95 from both sides)
-0.04t < -10 (divide both sides by -0.04)
t > 250
So plan A is cheaper than plan B when you send more than 250 texts.
Hope it helps.

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AskewTronics AskewTronics · Answer 2 · 2019-07-20T04:14:28+02:00

Answer:

Minimum number of messages to be sent is 251 for Plan A to be cheaper than Plan B.

Step-by-step explanation:

Let the text messages needed to be sent in order for Plan A to be cheaper than Plan B be N

Therefore total cost of sending text messages in case of Plan A is

[tex]C_A=\$ (30+0.01N)[/tex]

and total cost of sending text messages in case of Plan B is

[tex]C_B=\$ (20+0.05N)[/tex]

Now for Plan A to be cheaper than Plan B , [tex]C_A < C_B[/tex]

[tex]\therefore (30+0.01N)< (20+0.05N)=>N> 250[/tex]

Thus for Plan A to be cheaper than Plan B more than 250 messages needed to be sent . Minimum number of messages to be sent is 251 for Plan A to be cheaper than Plan B.