Question

A cell phone company charges a monthly fee of \(10 for the first 1000 text messages and 10 cents for each additional text message. Miriam’s bill for text messages for the month of June is \)38.50. How many text messages did she send that month?

Short answer

She will be sent 1285 messages that month.

Step-by-step solution

Step 1. Concept used.

$\text{Totalbill}=\left(\text{Monthlyfee}\right)+\left(\text{Extracharges}\right)$

Step 2. Plug the values in the total bill formula.

We have given

Monthly fee: $10 (first 1000 messages)

Extra charges: 10 cents times the number of additional messages is $0.10\left(t-1000\right)$.

Total bill: $38.50

Plug the values in the formula:

$38.50=10+0.10\left(t-1000\right)$

Step 3. Solve the equation.

We have

$38.50=10+0.10\left(t-1000\right)$

Apply distributive law:$a\left(b-c\right)=ab-bc$

$\begin{array}{l}38.50=10+0.10\cdot t-0.10\cdot 1000\\ 38.50=10+0.10t-100\\ 38.50=0.10t-90\end{array}$

Add 90 to both sides:

$\begin{array}{l}38.50+90=0.10t-90+90\\ 0.10t=128.50\end{array}$

Divide both sides by 0.10:

$\begin{array}{l}\frac{0.10t}{0.10}=\frac{128.50}{0.10}\\ t=1285\end{array}$

Hence, she will be sent 1285 messages at that month.