Question

1. extended response – comparing cell phone plans plan a charges $30 per month plus $0.10 per minute. plan b charges $45 per month plus $0.05 per minute.

a) write an equation for each plan.
b) solve to find the number of minutes where the cost is the same.
c) which plan is cheaper if you use 200 minutes? explain.

Explanation:

Step1: Write cost - equations

Let $x$ be the number of minutes.
For Plan A, the cost $C_A$ is $C_A = 30+0.10x$.
For Plan B, the cost $C_B$ is $C_B = 45 + 0.05x$.

Step2: Set costs equal and solve for $x$

Set $C_A=C_B$.
$30 + 0.10x=45+0.05x$.
Subtract $0.05x$ from both sides: $30 + 0.10x-0.05x=45+0.05x-0.05x$.
$30 + 0.05x=45$.
Subtract 30 from both sides: $30 - 30+0.05x=45 - 30$.
$0.05x=15$.
Divide both sides by 0.05: $x=\frac{15}{0.05}=300$.

Step3: Calculate costs for 200 minutes

For Plan A with $x = 200$: $C_A=30+0.10\times200=30 + 20=50$.
For Plan B with $x = 200$: $C_B=45+0.05\times200=45 + 10=55$.

Answer:

a) Plan A: $C_A = 30+0.10x$, Plan B: $C_B = 45 + 0.05x$.
b) 300 minutes.
c) Plan A is cheaper. When $x = 200$, $C_A=50$ and $C_B = 55$.