Question

classwork 10/15/2025 solve on a piece of paper and upload it to google classroom,1. a new cell phone company offers two monthly plansplan a: a flat fee of $25 per month plus $0.10 per text message.plan b: a flat fee of $40 per month plus $0.050 per text message.john wants to find out after how many text messages both plans cost the same amount andwhich plan is cheaper if they send more than that number of texts. verify the answer usingdesmos graph.2.two chess clubs offer different monthly payment options. iclub a : a $20 sign - up fee plus 415 per class.club b : a $50 sign - up fee plus $10 per class.carla wants to knowa. how many classes she must take for both clubs to cost the same.b. which club is cheaper if she takes 12 classes in a month.verify your answer using the desmos graph.

Explanation:

Step1: Set up equations for Plan A and Plan B

Let \(x\) be the number of text messages.
For Plan A, the cost \(C_A = 25+0.1x\).
For Plan B, the cost \(C_B=40 + 0.05x\).

Step2: Find when \(C_A = C_B\)

Set \(25+0.1x=40 + 0.05x\).
Subtract \(0.05x\) from both sides: \(25+0.1x-0.05x=40+0.05x - 0.05x\), so \(25 + 0.05x=40\).
Subtract 25 from both sides: \(0.05x=40 - 25\), so \(0.05x=15\).
Divide both sides by \(0.05\): \(x=\frac{15}{0.05}=300\).

Step3: Determine which plan is cheaper for \(x>300\)

Take \(x = 400\).
For Plan A: \(C_A=25+0.1\times400=25 + 40=65\).
For Plan B: \(C_B=40+0.05\times400=40+20 = 60\).
Since \(C_B300\), Plan B is cheaper when \(x>300\).

For the chess - club problem:

Part a

Let \(y\) be the number of classes.
For Club A, the cost \(C_A=20 + 15y\).
For Club B, the cost \(C_B=50+10y\).
Set \(20 + 15y=50+10y\).
Subtract \(10y\) from both sides: \(20+15y-10y=50+10y-10y\), so \(20 + 5y=50\).
Subtract 20 from both sides: \(5y=50 - 20\), so \(5y=30\).
Divide both sides by 5: \(y = 6\).

Part b

If \(y = 12\).
For Club A: \(C_A=20+15\times12=20+180=200\).
For Club B: \(C_B=50+10\times12=50+120=170\).
Since \(C_B

Answer:

1. The two cell - phone plans cost the same when there are \(300\) text messages. Plan B is cheaper when more than \(300\) text messages are sent.
2. a. Carla must take \(6\) classes for both chess - clubs to cost the same. b. Club B is cheaper if she takes \(12\) classes.