An overseas phone call is charged at one rate (a fixed amount) for the first minute
and at a different rate for each additional minute.
If a 7 minute call costs $10, and a 4 minute call costs $6.40, find each rate.
SOLUTION
This is a case of partial variation
C = a + k b
where C = cost of the call.
a = constant rate
k = per unit rate for a different rate for each additional minute.
when C= $10, b = 7
when C = $ 6. 40 , b = 4
10 = a + 7 k -------------- equ 1
6.40 = a + 4 k ................. equ 2
equation 1 minus equation 2 , we have :
10 - 6. 40 = 7 k - 4 k
3.60 = 3k
Divide both sides by 3 , we have :
k = 3. 60 / 3
k = 1.20
put k = 1. 20 in equ 1 , we have :
10 = a + 7 k
10 = a + 7 ( 1.20 )
10 = a + 8.40
a = 10 - 8. 40
a = 1. 60
CONCLUSION :
a = constant rate = $ 1.60 ( fixed amount) for the first minute.
k = per unit rate for a different rate for each additional minute = $ 1.20 per minute.