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Sagot :
For the Horizon offer
There is a cost of $45.99 for 700 minutes plus 6 cents for each additional minute
Since 1 dollar = 100 cents, then
6 cents = 6/100 = $0.06
If the total number of minutes is x, then
The total cost will be
[tex]C_H=45.99+(x-700)0.06\rightarrow(1)[/tex]For the Stingular offer
There is a cost of $29.99 for 700 minutes plus 35 cents for each additional minute
35 cents = 35/100 = $0.35
For the same number of minutes x
The total cost will be
[tex]C_S=29.99+(x-700)0.35\rightarrow(2)[/tex]For Horizon to be better that means, it cost less than the cost of Stingular
[tex]\begin{gathered} C_HSubstitute the expressions and solve for x[tex]\begin{gathered} 45.99+(x-700)0.06<29.99+(x-700)0.35 \\ 45.99+0.06x-42<29.99+0.35x-245 \\ (45.99-42)+0.06x<(29.99-245)+0.35x \\ 3.99+0.06x<-215.01+0.35x \end{gathered}[/tex]Add 215.01 to both sides
[tex]\begin{gathered} 3.99+215.01+0.06x<-215.01+215.01+0.35x \\ 219+0.06x<0.35x \end{gathered}[/tex]Subtract 0.06x from both sides
[tex]\begin{gathered} 219+0.06x-0.06x<0.35x-0.06x \\ 219<0.29x \end{gathered}[/tex]Divide both sides by 0.29 to find x
[tex]\begin{gathered} \frac{219}{0.29}<\frac{0.29x}{0.29} \\ 755.17Then x must be greater than 755.17The first whole number greater than 755.17 is 756
The total minutes should be 756 minutes per month for Horizon's to be the better deal.
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