A cell phone company charges a monthly fee of $20 for the first 1600 text messages and 40 cents for each additional text message. Miriam’s 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

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.




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:




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.



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

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