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.
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 ]
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