Question

a phone company offers two monthly plans. plan a costs $26 plus an additional $0.08 for each minute of calls. plan b has no initial fee but costs $0.13 for each minute of calls.
for what amount of calling do the two plans cost the same?
$\boldsymbol{square}$ minutes
what is the cost when the two plans cost the same?
$ $\boldsymbol{square}$

Explanation:

Step1: Define variables and cost equations

Let $x$ = number of calling minutes.
Cost of Plan A: $C_A = 26 + 0.08x$
Cost of Plan B: $C_B = 0.13x$

Step2: Set costs equal to solve for $x$

Set $C_A = C_B$:
$$26 + 0.08x = 0.13x$$
Subtract $0.08x$ from both sides:
$$26 = 0.13x - 0.08x$$
$$26 = 0.05x$$
Solve for $x$:
$$x = \frac{26}{0.05}$$
$$x = 520$$

Step3: Calculate equal cost

Substitute $x=520$ into $C_B$ (or $C_A$):
$$C = 0.13 \times 520$$
$$C = 67.60$$

Answer:

For 520 minutes, the two plans cost the same.
The cost when the two plans cost the same is $\$67.60$