Question

5a. Verizon charges a base fee of $20 per month plus an additional chargefor each minute the customer uses. The monthly phone cost, C, can berepresented with the equation C = 20 + a(m), where a is the additionalcharge per minute, and m is the number of minutes used. Which equationcan be utilized to find the number of minutes a customer used if we knowa and C?

Answer 1

a) Given the equation below

`C=20+a(m)`

Where

`\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}`

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

`\begin{gathered} C=20+a(m) \\ \text{Take 20 to the left handside} \\ C-20=a(m) \\ \text{Divide both sides by a} \\ (C-20)/(a)=(a(m))/(a) \\ m=(C-20)/(a) \end{gathered}`

Hence, the equation to find the number of minutes, m, a customer used is

`m=(C-20)/(a)`

The answer is option A

b) If Alicia pays $30 and used 500 minutes, to find the additional charges

That is

`\begin{gathered} C=\text{\$30} \\ m=500\text{minutes} \end{gathered}`

Substitute the values to find a

`\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} \\ (500a)/(500)=(10)/(500) \\ a=\text{ \$0.02} \end{gathered}`

Where 100 cents = 1 dollar

The additional charges, a = $0.02 in cents will be

`a=0.02*100=2\text{ cents}`

Hence, the additional charges, a, per minute used is 2 cents