a cell phone carrier offers two plans for text messaging. plan a costs $20 per month plus $0.05 per text…

a cell phone carrier offers two plans for text messaging. plan a costs $20 per month plus $0.05 per text. plan b costs $10 per month plus $0.10 per text. for how many text messages per month are the plans the same cost?\no 20\no 30\no 200\no 300

a cell phone carrier offers two plans for text messaging. plan a costs $20 per month plus $0.05 per text. plan b costs $10 per month plus $0.10 per text. for how many text messages per month are the plans the same cost?\no 20\no 30\no 200\no 300

Answer

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of text messages. The cost of Plan A, $C_A = 20+0.05x$. The cost of Plan B, $C_B=10 + 0.10x$.

Step2: Set the two equations equal

We want to find when $C_A = C_B$, so $20+0.05x=10 + 0.10x$.

Step3: Solve for $x$

Subtract $0.05x$ from both sides: $20=10 + 0.10x-0.05x$. Simplify to get $20=10 + 0.05x$. Then subtract 10 from both sides: $20 - 10=0.05x$, so $10 = 0.05x$. Divide both sides by 0.05: $x=\frac{10}{0.05}=200$.

Answer:

200