a cellular phone company offers a contract for which the cost C, in dollars of t minutes of telephoning is given c=0.25(t-300)+65.95 where it is assumed that t >== 300 minutes what times will keep costs between 106.20 and 139.20?
I am already lost at word problems... please help this is my last math problem.... I promise...
would it be 500 minutes??
No, you need two times, it asks for what times.
for 106.20 dollar
106.2=.25(t-300)+65.95
.25t=106.2-65.95+75
t=461 min. check that.
You do the other
Ok I got it it has to be betwee 461 and 593 minutes
No problem, I'm here to help! Let's break down the problem step by step.
Given information:
Cost equation: C = 0.25(t - 300) + 65.95
Range of costs: 106.20 <= C <= 139.20
Assumption: t >= 300 minutes
To find the times that keep costs between 106.20 and 139.20, we need to find the corresponding range of minutes (t).
Step 1: Substitute the lower cost limit (106.20) into the cost equation and solve for t:
106.20 = 0.25(t - 300) + 65.95
First, let's simplify the equation:
106.20 = 0.25t - 75 + 65.95
Combine like terms:
106.20 = 0.25t - 9.05
Next, let's isolate the variable by subtracting -9.05 from both sides:
106.20 + 9.05 = 0.25t
115.25 = 0.25t
Now, divide both sides by 0.25 to solve for t:
t = 115.25 / 0.25
t = 461
So, the lower limit of the minutes range is 461 minutes.
Step 2: Repeat the same process for the upper cost limit (139.20):
139.20 = 0.25(t - 300) + 65.95
First, simplify the equation:
139.20 = 0.25t - 75 + 65.95
Combine like terms:
139.20 = 0.25t - 9.05
Next, isolate the variable by subtracting -9.05 from both sides:
139.20 + 9.05 = 0.25t
148.25 = 0.25t
Now, divide both sides by 0.25 to solve for t:
t = 148.25 / 0.25
t = 593
So, the upper limit of the minutes range is 593 minutes.
Therefore, the times (t) that will keep costs between 106.20 and 139.20 are 461 minutes to 593 minutes.