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With cell phones being so common these days, the phone companies are all competung to earn business by offering various calling plans. 

 

One of them, horizon, offers 700 minutes of calls per month for $45.99, and additional minutes are charged at 6 cents per minute.

Another compary stingular, offers 700 minutes for $29.99 per month, and additional minutes are 35 cents each.

 

For how many total minutes of per month is horizon's plan a better deal?

 

Extra: A third company, Dash, offers a plan that costs $49 for 500 minutes, and extra minutes are 2 cents each. For how many total minutes of calls is the Dash plan the best deal of the three.

 

Please explain  and show your work multiple ways.

AloVera  Sep 22, 2018
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The equations for both plans are given by :

Horizon  = 45.99 +  .06x      where x is the number of minutes > 700

Singular = 29.99  + .35x

 

To find out where horzon's plan is the better deal, we need to solve this inequality

 

 

45.99  + .06x  <  29.99 + .35x        subtract  .06x, 29.99 from each side

 

16 < .29x   divide both sides by  .29

 

55.17 < x      [ Horizon's plan is better when the total minutes are  > 700 + 56 ≈   756 minutes ] 

 

 

Extra : 

 

 

Dash's plan can be modeled by   49 + .02x  where x is the number of minutes  > 500

However....this is for only 500 minutes...to equate the cost for 700 minutes, we need to add the cost for 200 additional minutes :

49  + .02 (200)  =  $53

 

So Dash's  plan for 700 minutes plus the additional charge of .02 / minute can be modeled by :

 

53 + .02x

 

So...to see where this is cheaper than Horizon's plan we have

 

53 + .02x  < 45.99 + .06x    subtract 45.99 , .02x  from  both sides

 

7.01  < .04x    divide both sides by .04

175.25 < x    [ Dash's plan is better than Horizon's when the total minutes  >  700 + 176 ≈  876 minutes ]

 

To find when Dash's plan is better than Singular's we have

 

53 + .02x  < 29.99 + 35x   subtract  .02x, 29.99  from  both sides

 

23.01 < .33x     divide both sides by .33

 

69.72 < x   [ Dash's plan is better than  Singular's when the total minutes >   700 + 70 ≈ 770 minutes  ]

 

So....Dash's  plan is the best when the number of minutes > 876

 

 

cool cool cool

CPhill  Sep 22, 2018

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