Given:
the plan of the pre-paid cell phone
The plan has a monthly fee and a charge for each minute
Let the monthly cost = C
and the number of minutes = x
the general equation will be:
C = ax + b
Where (b) is the monthly fee, and (a) is the charge per minute
We will find the values of (a) and (b) using the following:
1) 430 minutes cost $227.50
2) 780 minutes cost $385.00.
So, we have the following equations:
[tex]\begin{gathered} 430a+b=227.5\rightarrow(1) \\ 780a+b=385\rightarrow(2) \end{gathered}[/tex]
Solve the equations, subtract equation (1) from (2) to eliminate (b), and solve for (a):
[tex]\begin{gathered} 780a-430a=385-227.5 \\ 350a=157.5 \\ a=\frac{157.5}{350}=0.45 \end{gathered}[/tex]
Substitute with (a) into equation (1) to find the value of (b)
[tex]\begin{gathered} 430\cdot0.45+b=227.5 \\ 193.5+b=227.5 \\ b=227.5-193.5=34 \end{gathered}[/tex]
So, the equation of the monthly cost will be:
[tex]C=0.45x+34[/tex]
Part (b): When x = 484 minutes, we will find C
so, substitute with (x) into the equation of C
[tex]\begin{gathered} C=0.45\times484+34 \\ C=217.8+34 \\ C=251.8 \end{gathered}[/tex]
So, the answer will be:
A) C = 0.45x + 34
B) $251.8
