# Linear Equations

#### Jeanne1521

##### New member
Plan a charges $5.00 for the month plus$0.05/text message. Plan B charges $8.00 for the month plus$0.02/text message. After how many text messages will the plans cost the same?
I keep getting 0

#### lev888

##### Full Member
Plan a charges $5.00 for the month plus$0.05/text message. Plan B charges $8.00 for the month plus$0.02/text message. After how many text messages will the plans cost the same?
I keep getting 0
Please post your solution.

#### Jeanne1521

##### New member
I have y=5m+.05t and y=8m+.02t. When i input these into my graphing calculator and then go to the table, I get 0.

#### lev888

##### Full Member
I have y=5m+.05t and y=8m+.02t. When i input these into my graphing calculator and then go to the table, I get 0.
Are you solving for t or for m? 0 what?
I think it's asking after how many messages _each month_ the plans will cost the same _per month_. So I would set m to 1 and solve for t. Do you need to use a graphing calculator?

#### Jeanne1521

##### New member
The answer is how many texts can be sent that would make both plans the same amount. Solving for texts. I’m trying to use a graphing calculator but I seem to be stuck. Do I have to solve for messages first then get the texts?

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#### Jomo

##### Elite Member
Plan a charges $5.00 for the month plus$0.05/text message. Plan B charges $8.00 for the month plus$0.02/text message. After how many text messages will the plans cost the same?
I keep getting 0
Lets think about if your answer makes any sense (possibly you know it does not). You you have 0 text then plan a will charge you $5/month while plan B will charge you$8/month. Clearly different results.

Here is a common sense why of doing it. Plan B initial charge (ie no text charges) is $3 more than plan a. That is if you go with plan a you will save$3/month not taking into account text charges. Plan a charges you $0.03 more per text than plan B. Now for every text you make the sayings go down$0.03/month. Well 100 texts at $0.03 extra equals$3. So the answer is ____?

You want to know how many texts you can send per month (ie 1 Month) so the cost are equal.
Your equations should be C = 5+.05t and C=8+.02t. Now you can graph them and find the point of intersection. Did you notice that you can't graph C (or y) = 5m + .05t on a graph since there are three variables?

I got 100

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#### Otis

##### Senior Member
I got 100
Hi. That's correct. It's good form to answer word problems with a complete sentence. If you choose not to, at least include the units.

"At 100 text messages per month, the plans cost the same."

-or-

"100 texts"

#### Otis

##### Senior Member
… Do I have to solve for messages first then get the texts?
No -- "messages" and "texts" are the same thing.

When you wrote 5m + 0.03t earlier, I had thought you meant m=months, not messages. Both of those meanings are incorrect. 5 represents a dollar amount, so the expression 0.03t must also represent a dollar amount (otherwise, it would not make sense to add them).

5 + 0.03t is an expression that represents the cost (in dollars) of t texts in a month. We don't need the 'm'.