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The function for the cost of text messages is given by:
[tex]c=12.90+0.11t[/tex]If we have a total cost of $20, we then can solve for the number of text messages:
[tex]20=12.90+0.11t\Rightarrow20-12.90=0.11t[/tex]Dividing both sides of the equation by 0.11, we have:
[tex]\frac{7.1}{0.11}=t\Rightarrow t=64.5454\ldots[/tex]That is, for $20, Malcolm is able to send and receive about 64 message.