A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118. Find a linear equation for the monthly cost of the cell plan as a function of x, the number of monthly minutes used.

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berno berno · Answer 1 · 2020-10-07T21:47:06+02:00

Answer:

Linear equation for the monthly cost of the cell plan is [tex]10+0.15x[/tex]

Step-by-step explanation:

Let u denotes a flat monthly fee and v denotes amount charged per minute.

As the monthly cost is $71.50 if a customer uses 410 minutes,

[tex]71.50=u+410v[/tex] (i)

As the monthly cost is $118 if a customer uses 720 minutes,

[tex]118=u+720v[/tex] (ii)

Subtract (i) from (ii)

[tex]118-71.50=u+720v-u-410v\\46.5=310v\\v=\frac{46.5}{310}\\ v=0.15[/tex]

Put [tex]v=0.15[/tex] in (i)

[tex]71.50=u+410(0.15)\\71.50=u+61.5\\u=71.50-61.5\\u=10[/tex]

As x denotes the number of monthly minutes used,

linear equation for the monthly cost of the cell plan is [tex]10+0.15x[/tex]