Question

1. 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 than you must send to have the same cost for each of the plans.

Explanation:

Problem 3:

Step 1: Add $\frac{2}{7}m$ to both sides

To isolate the variable terms on one side, we add $\frac{2}{7}m$ to both sides of the equation $\frac{4}{7}m = 18-\frac{2}{7}m$.
$\frac{4}{7}m+\frac{2}{7}m = 18-\frac{2}{7}m+\frac{2}{7}m$
Simplifying the left side: $\frac{4 + 2}{7}m=\frac{6}{7}m$, and the right side: $18$ (since $-\frac{2}{7}m+\frac{2}{7}m = 0$)
So we get $\frac{6}{7}m=18$

Step 2: Multiply both sides by $\frac{7}{6}$

To solve for $m$, we multiply both sides of the equation $\frac{6}{7}m = 18$ by the reciprocal of $\frac{6}{7}$, which is $\frac{7}{6}$.
$m=18\times\frac{7}{6}$
Simplify $18\times\frac{7}{6}$: $18\div6 = 3$, so $3\times7=21$
So $m = 21$

Step 1: Define the variable

Let $x$ be the number of text messages.

Step 2: Write the cost equations for each plan

• For Plan A: The monthly fee is $\$15$ and the cost per text is $\$0.25$. So the total cost $C_A$ for Plan A is $C_A=15 + 0.25x$.
• For Plan B: The monthly fee is $\$20$ and the cost per text is $\$0.05$. So the total cost $C_B$ for Plan B is $C_B=20+0.05x$.

Step 3: Set the cost equations equal to each other

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

Step 4: Subtract $0.05x$ from both sides

To get the variable terms on one side, we subtract $0.05x$ from both sides.
$15+0.25x - 0.05x=20 + 0.05x-0.05x$
Simplifying: $15 + 0.2x=20$

Step 5: Subtract 15 from both sides

To isolate the term with $x$, we subtract 15 from both sides.
$15+0.2x - 15=20 - 15$
Simplifying: $0.2x = 5$

Step 6: Divide both sides by 0.2

To solve for $x$, we divide both sides of the equation $0.2x = 5$ by $0.2$.
$x=\frac{5}{0.2}$
$x = 25$

Answer:

$m = 21$

Problem 5: