A cellular phone company offers a contract for which is cost c,in dollars,of t minutes of telephoning is given by c=0.25(t-600)+61.95, where it is assumed that t>=600 minutes. What times will keep costs between #100.45 and $130.95?
To find the times that keep the costs between $100.45 and $130.95, we need to solve the given inequality equation.
The equation for the cost, c, in terms of the number of minutes, t, is:
c = 0.25(t - 600) + 61.95
We want to find the values of t that make the cost, c, between $100.45 and $130.95. So we have the following inequality:
100.45 <= 0.25(t - 600) + 61.95 <= 130.95
Let's simplify this inequality step by step:
Step 1: Subtract 61.95 from all three parts of the inequality:
100.45 - 61.95 <= 0.25(t - 600) <= 130.95 - 61.95
38.50 <= 0.25(t - 600) <= 69.00
Step 2: Divide all three parts of the inequality by 0.25 (the coefficient of (t - 600)):
38.50 / 0.25 <= (t - 600) <= 69.00 / 0.25
154 <= t - 600 <= 276
Step 3: Add 600 to all three parts of the inequality:
154 + 600 <= t <= 276 + 600
754 <= t <= 876
Therefore, the valid range of times that will keep the costs between $100.45 and $130.95 is t greater than or equal to 754 minutes and less than or equal to 876 minutes.