Question

International Plans A phone service provider offers two international plans.

Plan A: $\mathrm{\backslash (}25\text{permonthand5}\cancel{c}\text{perminute}$

Plan B:$\mathrm{\backslash )}5\text{permonthand12}\cancel{c}\text{perminute}$

For what range of minutes of international calls would plan B be financially advantageous?

Short answer

The range of minutes of international calls that make plan B is advantageous is to use less than 286 minutes.

Step-by-step solution

Step 1. Apply the concept of Solving linear inequalities.

An inequality looks like an equation, except that in the place of the equal sign is one of the symbols, $<,>,\le ,\ge$.

Example of an inequality is $4x+7\le 19$.

An inequality is linear if each term is constant or a multiple of the variable. To solve a linear inequality, isolate the variable on one side of the inequality sign.

Step 2. Find the inequality.

Let x be the number minutes.

Hence, the following are obtained:

$\begin{array}{l}\text{CostwithplanA:25+0.05x}\\ \text{CostwithplanB:5+0.12x}\end{array}$

Since plan B is advantageous than A so, B should be less than A. Hence,

$5+0.12x<25+0.05x$

Step 3. Simplify the inequality.

Simplify the inequality $5+0.12x<25+0.05x$. Therefore,

$\begin{array}{l}5+0.12x<25+0.05x\\ \Rightarrow 0.12x<25-5+0.05x\text{(subtract5)}\\ \Rightarrow 0.12x<20+0.05x\\ \Rightarrow 0.07x<20\text{(subtract0.05)}\end{array}$

Divide both sides by 0.07.

Hence,

$\begin{array}{l}x<\frac{20}{0.07}\\ x<\frac{2000}{7}\\ x<285.714\end{array}$

Therefore, the range of minutes of international calls that make plan B is advantageous is to use less than 286 minutes.