One cell phone plan costs $29.94 per month plus $.10 for each text message sent. another plan costs $32.99 per month plus $.05 for each text message sent. for what number of text messages will the monthly bill for both plans to be the same?

Answer

Find out the  For what number of text messages will the monthly bill for both plans to be the same .

To proof

Let us assume that the number of text messages per month be x.

As given

One cell phone plan costs $29.94 per month plus $.10 for each text message sent.

Another plan costs $32.99 per month plus $.05 for each text message sent.

than the equation becomes

29.94 + .10x = 32.99 + .05x

.10x - .05x = 32.99 - 29.94

0.05x = 3.05

x = 61

Hence the number of text messages will be 61 for which the monthly bill for both plans to be the same.

Hence proved

We are given:

One cell phone plan

Fix monthly charge =  $29.94 and

Per text message = $0.10

Therefore, equation for first cell phone:

y  = 0.10 x + 29.94      equation(1)

Where y is the total cost of the first cell phone plan each month for x number of text messages.

Another plan costs plan

Fix monthly charge =  $32.99 and

Per text message = $0.05

Therefore, equation for first cell phone:

y  = 0.05 x + 32.99     equation(2).

In order to find the number of text messages will the monthly bill for both plans to be the same, we need to set both equation equal and solve for x.

Therefore,

0.10 x + 29.94  = 0.05 x + 32.99  

Subtracting 29.94 from both sides, we get

0.10 x + 29.94 - 29.94  = 0.05 x + 32.99 - 29.94

0.10 x = 0.05x  + 3.05

Subtracting 0.05x from both sides, we get

0.10 x - 0.05 x = 0.05x- 0.05x  + 3.05

0.05x = 3.05.

Dividing both sides by 0.05, we get

x = 61.