Mathematical Inequality

Question

A cell phone provider offers one plan that charges $4.15 for the text messaging feature plus $0.09 for each individual incoming or outgoing text. Alternatively, the provider offers a second plan with a flat rate of $19.00 for unlimited text messaging how many text messages.How many text messages woulf result in the unlimited option being the better deal?

 

If there were more or less than______ text messages, the unlimited option would be the better deal.

Answer 1

PROBLEM

 

Mathematical Inequality
A cell phone provider offers one plan that charges $4.15 for the text messaging feature plus $0.09 for each individual incoming or outgoing text. Alternatively, the provider offers a second plan with a flat rate of $19.00 for unlimited text messaging how many text messages.How many text messages woulf result in the unlimited option being the better deal?

If there were more or less than______ text messages, the unlimited option would be the better deal.

 

SOLUTION

 

Set up the inequality as follows:

 

A better deal means you pay less money. Therefore, since you want to know when the flat rate unlimited text option (option 2 price) is the better deal, it would have to cost less than the base rate plus per text charge option (option 1 price). You would then say set up the inequality based on costs as follows...

 

Option 1 price = 4.15 + 0.09t (t is the number of text messages)

Option 2 price = 19.00

 

For the better deal, Option 2 price < Option 1 price

 

Now substitute the two expressions for Option 1 price and Option 2 price into the inequality above and solve for t.