T-Mobile Fought Sprint — Customers Declared The Winner

Algebra Level 1

In an effort to capture market share of the wireless mobile phone network in USA, Sprint and T-Mobile have pursued extremely aggressive phone plan pricing. Both companies are offering unlimited talk, text and data for the customers, who are further encouraged to group up and form €˜family plans to benefit from further cost savings.

For T-Mobile customers, the first line costs $70, adding the second line costs an additional $30, and any lines after that cost an additional $10 each.

For Sprint customers, the first line costs $50, adding the second line costs an additional $40, adding the third line costs an additional $30 and any lines after that cost an additional $20 each.

If I want to purchase a family plan with 4 lines, which service provider has the cheaper plan?

Neither; they are the same. Sprint T-Mobile AT&T

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14 solutions

Prasun Biswas
Feb 3, 2014

According to the picture, T-Mobile has prices(in $ ) = 70 , 30 , 10 , 10 , . . . . \$)=70,30,10,10,.... for 1st line, 2nd line, 3rd line, 4th line and so on respectively while Sprint has prices(in $ ) = 50 , 40 , 30 , 20 , . . . . \$)=50,40,30,20,.... for 1st line, 2nd line, 3rd line, 4th line and so on. If we take 4 lines, then we have the total cost for purchasing a family plan with 4 lines as follows ----

For T-Mobile users = $ ( 70 + 30 + 10 + 10 ) = $ 120 =\$(70+30+10+10)=\$120

For Sprint users = $ ( 50 + 40 + 30 + 20 ) = $ 140 =\$(50+40+30+20)=\$140 .

So, clearly we can see that T-Mobile has the cheapest plan.

actually it's like-for T-mobile users=$[70+(70+30)+(70+30+10)+(70+30+10+10)]

Ravi Mahar - 7 years, 4 months ago

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I dont think so because if that's the case, then we get equal prices for both companies and none of them will be cheaper than the other. If your insight is considered then we get ---

For T-Mobile = $ [ ( 70 + ( 70 + 30 ) + ( 70 + 30 + 10 ) + ( 70 + 30 + 10 + 10 ) ] =\$[(70+(70+30)+(70+30+10)+(70+30+10+10)]

= $ ( 70 + 100 + 110 + 120 ) = $ 400 =\$(70+100+110+120)=\$\boxed{400}

For Sprint = $ [ ( 50 + ( 50 + 40 ) + ( 50 + 40 + 30 ) + ( 50 + 40 + 30 + 20 ) ] =\$[(50+(50+40)+(50+40+30)+(50+40+30+20)]

= $ ( 50 + 90 + 120 + 140 ) = $ 400 =\$(50+90+120+140)=\$\boxed{400}

Then, we dont get any cheaper plan as both would cost $ 400 \$400 , so I think your insight is wrong. Hope this helps .... :)

Prasun Biswas - 7 years, 4 months ago

this is best :)

Sowmy Vivek - 7 years, 4 months ago

If someone want to purchase a mobile family plan with 4 lines, T-Mobile and Sprint are service providers that offer these plans and:

For T-Mobile customers, the first line costs $70, adding the second line costs an additional $30, and any lines after that cost an additional $10 each, so 4 lines cost $70 + $30 + $10 + $10 = $120;

For Sprint customers, the first line costs $50, adding the second line costs an additional $40, adding the third line costs an additional $30 and any lines after that cost an additional $20 each, so 4 lines cost $50 + $40 + $30 + $20 = $140.

So, the service provider that has the cheaper plan is T-Mobile because your plan of 4 lines is $140 - $120 = $20 cheaper than Sprint.

Ivy Joy Barrion
Feb 12, 2014

T-Mobile = 70 + 30 + 10 +10 = 120 While, Spring = 50 + 40 +30 + 20 = 140

This is very simple!

Just sum all the price between T-MOBILE and SPRINT and choose which one is cheaper plan..

for T-MOBILE 70 + 30 + 10 + 10 × 7 = 180 70+30+10+10 \times 7=180

for SPRINT 50 + 40 + 30 + 20 × 7 = 290 50+40+30+20 \times 7=290

We can see that T-MOBILE is cheaper plan than SPRINT

Wouldn't it be:

for T-Mobile: 70 + 30 + 10 + 10 = 120 70 + 30 + 10 + 10 = 120 ,

and for Sprint: 50 + 40 + 30 + 20 = 140 50 + 40 + 30 + 20 = 140

Captain Ahab - 7 years, 4 months ago

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You have to pay your attention to upper word. It's word: 1st PHONE,2nd PHONE, 3rd PHONE, PHONES 4-10. you know what it is mean? there are 10 periods of phone right there.

Hafizh Ahsan Permana - 7 years, 4 months ago

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You are mistaken. The column shows "PHONES 4-10" but the question is about cheaper plan for a family plan with 4 lines so you dont have to consider the rest of the 6 phone lines as you are not purchasing them.

Prasun Biswas - 7 years, 4 months ago

t has 1st line costly only

M SAJID IQBAL - 7 years, 4 months ago
Dik Va
Feb 14, 2014

it is cheaper because if we add the total of t-mobile it is cheaper than sprint mobile

Laura Lopez
Feb 12, 2014

By calculating the total of both services we can see that Tmobile is $110 and Sprint $140 , so Tmobile is cheaper

since T mobile cost 120$ for four lines ,sprint cost 140$ for four lines,even combination doesn't work well,hence T mobile is the cheapest option.

Tallal Jamshed
Feb 1, 2014

add all the numbers together T_mobile = 120 sprint = 140

Tshering Tashi
Jan 31, 2014

Add all the package for T - Mobile its $120 and all the package for Sprint is $140 so T- Mobile is better

Pradyut Singh
Jan 31, 2014

ONLY CALCULATE FOUR LINE FOR BOTH PHONE....

Arif Stanekzai
Jan 30, 2014

If you buy sprint mobile compare to T mobile you well have to spent 20$ more so t mobile is cheaper :P

Rachit Agarwal
Jan 29, 2014

calculate the 4 price ( add them) now compare price of both

Hashfa Hussain
Jan 28, 2014

Apparently T-Mobile is consuming more amount in buying the first mobile, however, with the purchase of further units the cost is going to be decreased accordingly. It is therefore recommended that if any one wants to purchase 04 units then he is supposed to buy T-Mobile

SIR I WANT TO ABOUT SOMETHING TO YOUR GROUP

Dinesh Sharma - 7 years, 4 months ago
Raj Error
Jan 27, 2014

WHAT'S AT&T?? :D

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