How many text messages before they are the same

Question

Ciera pays $15 a month plus .15 a text message for her cell phone. Alexis pays $20 a month plus .05 a text message. After how many text messages will the cost be the same for both companies?

Answer 1

Ciera: cost = 15 + 0.15x

Alexis cost = 20 + 0.05x

The questions asks for how many texts until they are the same. Therefore, we can set both equations equal to each other and solve for x.

15 + 0.15x = 20 + 0.05x subtract 15 from both sides

0.15x = 5 + 0.05x subtract 0.05x from both sides

0.10x = 5 divide both sides by 0.10

x = 50

At 50 text messages, both will have the same cost.

Answer 2

Ciera pays $15 a month plus .15 a text message for her cell phone. Alexis pays $20 a month plus .05 a text message. After how many text messages will the cost be the same for both companies?

Let x = the number of text messages sent.

Ciera: 15+0.15x

Alexis: 20+0.05x

Now set them equal to find the value of x where the cost is the same

15+0.15x=20+0.05x Subtract 15 from both sides of the equation

15+0.15x-15=20+0.05x-15 Simplify

0.15x=5+0.05x Subtract 0.05x from both sides

0.15x-0.05x=5+0.05x-0.05x Simplify

0.10x=5 Divide both sides by 0.10

0.10x/.10=5/.10

x= 50 text messages the cost will be the same

Answer 3

Ciera pays $15 a month plus .15 a text message for her cell phone. Alexis pays $20 a month plus .05 a text message. After how many text messages will the cost be the same for both companies?

Let "n" be the number of text messages.

Then Ciera's cost is 15 + 0.15n

And Alexis' cost is 20 + 0.05n

Their costs are the same when:

15 + 0.15n = 20 + 0.05n [subtract 15 from both sides to get:

0.15n = 5 + 0.05n [subtract 0.05n from both sides to get:

0.10n = 5 [divide both sides by 0.10 to get

n = 50 so 50 text messages result in their costs being the same.

As a check, Ciera's cost is 15 + 0.15•50 = 15 + 7.50 = $22.50

Alexis's cost is 20 + 0.05•50 = 20 + 2.50 = $22.50