Studdy AI Logo
Math

QuestionCompare two phone plans: Family Plan (81+46P81 + 46P) and Mobile Share Plan (129+34P129 + 34P). Find when costs are equal and which is better for 5 devices.

Studdy Solution

STEP 1

Assumptions1. The Family Plan has a monthly fee of 81,unlimitedtalkandtextonupto5lines,anddatachargesof81, unlimited talk and text on up to5 lines, and data charges of 46 for each device for up to GB of data per device. . The Mobile Share Plan has a monthly fee of 129forupto10devices,unlimitedtalkandtextforallthelines,anddatachargesof129 for up to10 devices, unlimited talk and text for all the lines, and data charges of 34 for each device up to a shared total of10 GB of data.
3. We use $$ to represent the number of devices that need data plans as part of their cost.
4. We assume that the users stay under their data limit.

STEP 2

First, we need to find the model of the total cost of the Family Plan. The total cost consists of the monthly fee and the data charges for each device.
Family Plan Cost=Monthly fee+Data charges per device×Number of devicesFamily\, Plan\, Cost = Monthly\, fee + Data\, charges\, per\, device \times Number\, of\, devices

STEP 3

Now, plug in the given values for the monthly fee, data charges per device, and number of devices to get the model of the total cost of the Family Plan.
Family Plan Cost=$81+$46×Family\, Plan\, Cost = \$81 + \$46 \times

STEP 4

Next, we need to find the model of the total cost of the Mobile Share Plan. The total cost consists of the monthly fee and the data charges for each device.
Mobile Share Plan Cost=Monthly fee+Data charges per device×Number of devicesMobile\, Share\, Plan\, Cost = Monthly\, fee + Data\, charges\, per\, device \times Number\, of\, devices

STEP 5

Now, plug in the given values for the monthly fee, data charges per device, and number of devices to get the model of the total cost of the Mobile Share Plan.
Mobile Share Plan Cost=$129+$34×Mobile\, Share\, Plan\, Cost = \$129 + \$34 \times

STEP 6

To find the number of devices that would make the two plans equal in cost, we set the cost of the Family Plan equal to the cost of the Mobile Share Plan and solve for $$.
$81+$46×=$129+$34×\$81 + \$46 \times = \$129 + \$34 \times

STEP 7

Subtract \$81 from both sides of the equation.
$46×=$129+$34×−$81\$46 \times = \$129 + \$34 \times - \$81

STEP 8

Subtract \$34 \times from both sides of the equation.
$46×−$34×=$129−$81\$46 \times - \$34 \times = \$129 - \$81

STEP 9

implify both sides of the equation.
$12×=$48\$12 \times = \$48

STEP 10

Divide both sides of the equation by \12tosolvefor12 to solve for $.
=$48/$12 = \$48 / \$12

STEP 11

Calculate the value of $$.
=$48/$=4 = \$48 / \$ =4So, for4 devices, both plans would cost the same.

STEP 12

If a family has5 smart phones, we need to calculate the cost for both plans and compare them.
For the Family PlanFamily Plan Cost=$81+$46×5Family\, Plan\, Cost = \$81 + \$46 \times5For the Mobile Share PlanMobile Share Plan Cost=$129+$34×5Mobile\, Share\, Plan\, Cost = \$129 + \$34 \times5

STEP 13

Calculate the cost for both plans.
For the Family PlanFamily Plan Cost=$81+$46×5=$315Family\, Plan\, Cost = \$81 + \$46 \times5 = \$315For the Mobile Share PlanMobile Share Plan Cost=$129+$34×5=$299Mobile\, Share\, Plan\, Cost = \$129 + \$34 \times5 = \$299So, for a family with5 smart phones, the Mobile Share Plan is cheaper.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord