Answer :
Answer
The monthly cost for 72 minues of calls = $15.15
Explanation
Let the monthly cost in dollars of the long distance phone plan be represented by y.
Let the total calling time in minutes be represented by x.
We are told that montly cost in dollars of the long distance phone plan, y, is a linear function of the total calling time in minute, x. In mathematical terms and using the equation of a straight line model,
y = a + bx
where
a = fixed amount paid monthly
b = dollar per unit time rate charged on the calls
when x = 49 minutes, y = 13.08 dollars
13.08 = a + 49b ........... equation 1
when x = 86 minutes, y = 16.41 dollars
16.41 = a + 86b ........... equation 2
Combining these simultaneous equations
a + 49b = 13.08 .............. equation 1
a + 86b = 16.41 .............. equation 2
Subtract equation 1 from equation 2
a - a + 86b - 49b = 16.41 - 13.08
37b = 3.33
Divide both sides by 37
(37b/37) = (3.33/37)
b = 0.09 dollars per minute.
We can now solve for a
when b = 0.09
a + 49b = 13.08
a + 49(0.09) = 13.08
a + 4.41 = 13.08
a = 13.08 - 4.41
a = 8.67 dollars
So, the linear function that relates the montly cost in dollars of the long distance phone plan, y, to the total calling time in minute, x is
y = a + bx
a = $8.67 and b = $0.09 per minute
y = 8.67 + 0.09x
When total calling time in minutes, x = 72 minutes, we can now calculate the monthly cost, y.
y = 8.67 + 0.09x
y = 8.67 + 0.09(72)
y = 8.67 + 6.48
y = $15.15
Hope this Helps!!!
