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Questions 56
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 #1
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+1

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

22 sept. 2018