a cellular phone company offers a contract for which the cost C, in dollars, of t minutes of telephoning is given by C=0.25(t-600) + 43.95, whe it is assumed that t¡Ý 600 minutes. What time will keep costs between $82.95 and $110.95?
For the cost to be between $82.95 and $110.95, the telephoning time must be between minutes and minutes
Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $180.00 of her medical bills, plus 35% of the rest. Under plan B, Giselle would pay the first $210.00, but only 25 % of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $210.00 in bills.
Giselle would save with plan B if she had more than $________ in bills
Does t¡Ý 600 mean t > 600 ?
Set the cost equation equal to 82.95 and solve for the number of minutes, t. Then do it again for a cost of 110.95. That will give you the minimum and maximum times that they want.
In the last problem, set the amount of bills equal to X. The the amounts paid under either plan are the same,
180 + 0.35 X = 210 + 0.25 X
This leads to
0.1 X = 30.
Solve for the X for which the plans cost the same. Plan B saves the most money for higher bills.
To find the time that will keep costs between $82.95 and $110.95, we need to set up an inequality using the given cost equation.
Given:
C = 0.25(t - 600) + 43.95
82.95 ≤ C ≤ 110.95
Substitute the value of C into the inequality:
82.95 ≤ 0.25(t - 600) + 43.95 ≤ 110.95
Simplify the inequality:
82.95 - 43.95 ≤ 0.25(t - 600) ≤ 110.95 - 43.95
Combine like terms:
39 ≤ 0.25(t - 600) ≤ 67
Divide all terms by 0.25:
(39/0.25) ≤ t - 600 ≤ (67/0.25)
Simplify:
156 ≤ t - 600 ≤ 268
Add 600 to all terms:
156 + 600 ≤ t - 600 + 600 ≤ 268 + 600
Simplify:
756 ≤ t ≤ 868
Therefore, the telephoning time must be between 756 minutes and 868 minutes to keep costs between $82.95 and $110.95.
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For the health insurance problem, to find the amount of medical bills where Plan B saves Giselle money, we need to set up an equation by comparing the costs under both plans.
Let x be the amount of medical bills.
Plan A cost = $180.00 + 35% of (x - $180.00)
Plan B cost = $210.00 + 25% of (x - $210.00)
Plan B would save Giselle money if Plan B cost < Plan A cost:
$210.00 + 25% of (x - $210.00) < $180.00 + 35% of (x - $180.00)
First, remove the percentages by converting them to decimals:
$210.00 + 0.25(x - $210.00) < $180.00 + 0.35(x - $180.00)
Simplify and distribute:
$210.00 + 0.25x - $52.50 < $180.00 + 0.35x - $63.00
Combine like terms and solve for x:
$157.50 + 0.25x < $117.00 + 0.35x
Subtract 0.25x from both sides:
$157.50 < $117.00 + 0.10x
Subtract $117.00 from both sides:
$40.50 < 0.10x
Divide both sides by 0.10:
$405.00 < x
Therefore, Giselle would save with Plan B if she had more than $405.00 in medical bills.