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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
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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

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