Question

your cellular telephone provider offers two plans. plan a has a monthly fee of $15 and $0.25 per text. plan b has a monthly fee of $20 and $0.05 per text. write and solve an equation to find the number of texts that you must send to have the same cost for each of the plans.

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of texts. The cost of Plan A, $C_A=15 + 0.25x$. The cost of Plan B, $C_B=20+0.05x$.

Step2: Set the two equations equal

We want to find when $C_A = C_B$, so we set up the equation $15 + 0.25x=20 + 0.05x$.

Step3: Solve for $x$

First, subtract $0.05x$ from both sides: $15 + 0.25x-0.05x=20+0.05x - 0.05x$, which simplifies to $15 + 0.2x=20$. Then subtract 15 from both sides: $15-15 + 0.2x=20 - 15$, giving $0.2x=5$. Finally, divide both sides by 0.2: $x=\frac{5}{0.2}=25$.

Answer:

25