Example 1 :
The cost C of hiring a squash court for h hours is given by
C = 12h + 5
dollars. Find the cost of hiring a court for :
a) 1 hour
b) 30 mins
c) 1 hour 15 mins.
Solution :
C = Cost of hiring a squash court
h = hours taken
(a) To find cost for 1 hour, we apply h = 1
C = 12(1) + 5
C = 12+5
C = $17
Cost for hiring a court for 1 hour is $17.
(b) To find cost for 30 minutes, we apply h = 1/2
C = 12(1/2) + 5
C = 6+5
C = $11
Cost for hiring a court for 30 minutes is $11.
(c) 1 hour 15 minutes = 60 + 15
= 75 minutes
= 75/60
= 15/12
= 5/4 hour
C = 12(5/4) + 5
C = 15+5
C = $20
Cost for hiring a court for 1 hour and 15 minutes is $20.
Example 2 :
The volume of water in a tank t minutes after a tap is switched on, is given by
V = 5000 - 20t liters.
a) Find V when t = 0. What does this mean?
b) Find the volume of water left in the tank after:
i) 5 minutes
ii) 1 hour
iii) 3 1/2 hours.
Solution :
(a) When t = 0
V = 5000 - 20(0)
V = 5000
Before the tap switched on, volume of water in the tank is 5000 liter.
(b)
V = 5000 - 20t
(i) when t = 5 V = 5000-20(5) V = 5000-100 V = 4900 liter |
(ii) when t = 1 V = 5000-20(1) V = 5000-20 V = 4980 liter |
(iii) when t = 3 1/2 ==> 7/2
V = 5000-20(7/2)
V = 5000-70
V = 4930 liter
Example 3 :
To add the whole numbers from 1 to n we can use the formula
Sn = n(n+1)/2
Use the formula to add all the whole numbers from 1 up to:
i) 50
ii) 200
iii) 1000
Solution :
(i) To find the sum of numbers from 1 to 50,
we apply n = 50
S50 = 50(50+1)/2
S50 = 25 x 51
S50 = 1275
(ii) To find the sum of numbers from 1 to 200,
we apply n = 200
S200 = 200(200+1)/2
S200 = 100 x 201
S200 = 20100
(iii) To find the sum of numbers from 1 to 1000,
we apply n = 1000
S1000 = 1000(1000+1)/2
S1000 = 500 x 1001
S1000 = 500500
Example 4 :
Michelle has $2000 in a bank account. Each week she deposits a further $120.
a) Explain why the amount of money in her account after n weeks is given by
M = 2000 + 120n pounds.
b) How much money does she have in her bank account after :
i) 3 weeks
ii) 6 months
iii) 1 1/2 years?
Solution :
(a) Every week he is depositing 120.
if n = 0, M = 2000 (Already he has)
if n = 1, M = 2120 (he has 2120)
if n = 1, M = 2240 (he has 2240).........
(b) If n = 3
M = 2000 + 120(3)
M = 2000 + 360
M = 2360 pounds
(ii) 6 months = 24 weeks
M = 2000 + 120(24)
M = 2000 + 2880
M = 4880 pounds
If n = 6
M = 2000 + 120(6)
M = 2000 + 720
M = 2720 pounds
(iii) 1 1/2 years
1 year + 6 months = 52 + 24
= 76 weeks
M = 2000 + 120(76)
M = 2000 + 9120
M = 11120 pounds
Example 5 :
The cost C of hiring a room for a function is given by
C = 150 + 30g
euros where g is the number of guests. Find the cost of hiring the room for :
a) 20 guests
b) 50 guests
c) 90 guests
Solution :
(a) g = 20
C = 150 + 30(20)
C = 150 + 600
C = 750
So, the cost of hiring the room for 20 guests is $750.
(b) g = 50
C = 150 + 30(50)
C = 150 + 1500
C = 1650
So, the cost of hiring the room for 50 guests is $1650.
(c) g = 90
C = 150 + 30(90)
C = 150 + 2700
C = 2850
So, the cost of hiring the room for 90 guests is $2850.
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