Question

A cell phone company has two different cell phone plans, as shown below:

PLAN A: $35 monthly charge + 10 cents per text message
PLAN B: $18 monthly charge + 20 cents per text message

1. Write a system of equations to describe the two cell phone plans. Identify each variable used in your equations.

2. If you plan on sending 65 text messages per month, how much would you pay for one month under each plan? Show your work.

PLAN A: _______
PLAN B:________

3. How many text messages would you need to send in one month for the two plans to cost the same? Show your work.

Answer 1

1. 35+0.10x
18+0.20x

2. 35+0.10(65)=35+6.5=41.5
18+0.20(65)=18+13=31
Plan A: $41.5
Plan B: $31

3. 35+0.10x=18+0.20x
17+0.10x=0.20x
17=0.10x
170=x
170 texts

Answer 2

170 text messages

Explanation:

1. Let's define the variables:

Let x be the number of text messages sent per month.

Let C_A be the cost for Plan A.

Let C_B be the cost for Plan B.

The system of equations describing the two cell phone plans is:

For Plan A: C_A = 35 + 0.10x

For Plan B: C_B = 18 + 0.20x

2. For Plan A:

C_A = 35 + 0.10 * 65 = $41.50

For Plan B:

C_B = 18 + 0.20 * 65 = $31.00

3. To find the point at which the two plans cost the same (C_A = C_B):

35 + 0.10x = 18 + 0.20x

0.10x = 17

x = 170

So, you would need to send 170 text messages in one month for the two plans to cost the same.