A cell phone company charges a monthly fee of $20 for the first 1600 text messages and 40 cents for each additional text message. MiriamÂs bill for text messages for the month of June is $42.80. How many text messages did she send that month?

Guest May 22, 2017

#1**+1 **

Mariama sent 1657 text messages during June.

Okay, the situation you have mentioned above can be represented as a linear expression;

Let t=amount of text messages above 1600.

\($20+0.4t\)

In the expression above you pay $20 for every text message until Mariama surpasses 1600 texts. Once that happens, Mariama is charged 40 cents for every additional text message. Set this expression equal to the bill, $42.80, and solve:

\($20+0.4t=$42.80\)

For ease of calculation, I will get rid of that decimal by converting to a fraction:

\($20+\frac{4}{10}t=$42.80\) Multiply by 10 on each side to get rid of the fraction, which eases solving significantly.

\(200+4t=428\) Subtract 200 on both sides.

\(4t=228\) Divide by 4 to isolate t, the number of texts.

\(t=57\)

Wait! We aren't done yet! 57 is the number of texts made over the allotted 1600. Add 57 to 1600 and then you are done.

\(1600+57=1657\) texts made during the month of June.

TheXSquaredFactor
May 22, 2017