Respuesta :
a) Given the equation below
[tex]C=20+a(m)[/tex]Where
[tex]\begin{gathered} C\text{ is the monthly phone cost} \\ a\text{ is the additional charge per minute} \\ \text{m is the number of minutes used} \end{gathered}[/tex]The equation that can be utilized to find the number of minutes used by a customer can be represented by making m the subject
The equation can be deduced below
[tex]\begin{gathered} C=20+a(m) \\ \text{Take 20 to the left handside} \\ C-20=a(m) \\ \text{Divide both sides by a} \\ \frac{C-20}{a}=\frac{a(m)}{a} \\ m=\frac{C-20}{a} \end{gathered}[/tex]Hence, the equation to find the number of minutes, m, a customer used is
[tex]m=\frac{C-20}{a}[/tex]The answer is option A
b) If Alicia pays $30 and used 500 minutes, to find the additional charges
That is
[tex]\begin{gathered} C=\text{\$30} \\ m=500\text{minutes} \end{gathered}[/tex]Substitute the values to find a
[tex]\begin{gathered} C=20+a(m) \\ 30=20+a(500) \\ \text{Collect like terms} \\ 30-20=500a \\ 10=500a \\ \text{Divide both sides by 500} \\ \frac{500a}{500}=\frac{10}{500} \\ a=\text{ \$0.02} \end{gathered}[/tex]Where 100 cents = 1 dollar
The additional charges, a = $0.02 in cents will be
[tex]a=0.02\times100=2\text{ cents}[/tex]Hence, the additional charges, a, per minute used is 2 cents
