QuestionCompare costs of two phone plans: Family Plan: \$98 + \$39P (up to 5 lines) vs. Mobile Share Plan: \$122 + \$35P (up to 10 lines). Find P for equal costs and recommend for 5 devices.

Studdy Solution

STEP 1

Assumptions1. The Family Plan has a monthly fee of $98, unlimited talk and text on up to5 lines, and data charges of$ 39 for each device for up to GB of data per device. . The Mobile Share Plan has a monthly fee of $122 for up to10 devices, unlimited talk and text for all the lines, and data charges of$ 35 for each device up to a shared total of10 GB of data.
3. We denote the number of devices that need data plans as part of their cost by $$.
4. We assume that they stay under their data limit.

STEP 2

First, we need to find the model of the total cost of the Family Plan. We can do this by adding the monthly fee to the product of the number of devices and the data charge per device.
$Family\, Plan\, Cost = Monthly\, fee + (Number\, of\, devices \\times Data\, charge\, per\, device)$

STEP 3

Now, plug in the given values for the monthly fee, number of devices, and data charge per device to find the model of the total cost of the Family Plan.
$Family\, Plan\, Cost = \$98 + ( \\times \$39)$

STEP 4

Next, we need to find the model of the total cost of the Mobile Share Plan. We can do this by adding the monthly fee to the product of the number of devices and the data charge per device.
$Mobile\, Share\, Plan\, Cost = Monthly\, fee + (Number\, of\, devices \\times Data\, charge\, per\, device)$

STEP 5

Now, plug in the given values for the monthly fee, number of devices, and data charge per device to find the model of the total cost of the Mobile Share Plan.
$Mobile\, Share\, Plan\, Cost = \$122 + ( \\times \$35)$

STEP 6

To find the number of devices that would make the two plans equal in cost, we need to set the two cost models equal to each other and solve for $$.
$\$98 + ( \\times \$39) = \$122 + ( \\times \$35)$

STEP 7

Subtract \$98 from both sides of the equation.
$\\times \$39 = \$24 + \\times \$35$

STEP 8

Subtract $\\times \$35$ from both sides of the equation.
$\\times \$4 = \$24$

STEP 9

Divide both sides of the equation by \ $4 to solve for$ $.
$= \$24 / \$4$

STEP 10

Calculate the value of $$.
$= \$24 / \$4 =6$ So, the two plans would be equal in cost for6 devices.

STEP 11

If a family has5 smart phones, we need to calculate the cost for each plan and compare them. First, calculate the cost for the Family Plan.
$Family\, Plan\, Cost = \$98 + (5 \\times \$39)$

STEP 12

Calculate the cost for the Family Plan.
$Family\, Plan\, Cost = \$98 + (5 \\times \$39) = \$293$

STEP 13

Next, calculate the cost for the Mobile Share Plan.
$Mobile\, Share\, Plan\, Cost = \$122 + (5 \\times \$35)$

STEP 14

Calculate the cost for the Mobile Share Plan.
$Mobile\, Share\, Plan\, Cost = \$122 + ( \\times \$35) = \$297$ Since the Family Plan costs \$293 and the Mobile Share Plan costs \$297, the family should choose the Family Plan because it is cheaper.

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