Question

A cell phone provider offers a plan that costs $40 per month plus $20 per text message sent or received. A comparable plan costs $70 per month but offers unlimited text messaging. How many text messages would have to be sent or received in order for the plans to cost the same?

Answer 1

x = 150 text message

Explanation:

Let x be the number of the text message.

Given:

First plan = $40 per month plus $0.20 per text message

Second plan = $70 per month with unlimited messaging

Solution:

According to given statement the cost of the first plan is $40 per month plus $0.20 per text message and other plan is $70 per month with unlimited messaging.

So, we write the equation as:

`40+0.20(x)=70`

Subtract 40 from both side.

`40+0.20(x)-40=70-40`

`0.20(x)=30`

Divide both side by 0.20

`x = (30)/(0.20)`

x = 150 text message

Therefore, 150 text messages should be sent or received in order for the plans to cost the same.

Answer 2

A cell phone provider offers a plan that costs $40 per month plus $0.20 per text message sent or received. A comparable plan costs $70 per month but offers unlimited text messaging.

How many text messages would you have to send or receive in order for the plans to cost the same each month?

Number of text messages to be sent or received = 150

Explanation:

Given:

Cost of the first plan, excluding message charges = $40

Cost of the second plan including message charges = $70

Cost of one text message = $0.20

The second plan offers unlimited text messaging.So we have to find the number of text messages to which the plan cost the same that is exactly $70.

Let the number of messages be 'x'

Total cost of messages = 0.2(x)

Plan with $0.20 text messages can be written as 40+0.20(x).

Set both the plan equal to each other to find the number of messages.

Re-arranging it into equation:

⇒
`40+0.2(x)= 70`

⇒
`0.2(x)=70-40`

⇒
`0.2(x)=30`

⇒
`x=(30)/(0.2)`

⇒
`x=150`

So,

The number of text messages to be sent or received = 150,which will cost the plan to be same of $70.