Example 1 :
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 her in bank account after :
(i) 3weeks (ii) 6 months (iii) 1 1/2 years ?
Solution :
a) The amount he already has in his account = $2000
Each week she deposits = $120
According to above statement,
After 1 week, she has 2000 + 120 × 1
After 2 weeks, she has 2000 + 120 × 2
After 3 weeks, she has 2000 + 120 × 3
...........................
After n weeks, she has 2000 + 120 × n
So, M = 2000 + 120n
(where M is the amount of money and n is the number of weeks)
b) (i) Given, n = 3 weeks
Amount of money (M) = 2000 + 120n
M = 2000 + 120(3)
M = 2360 pounds
So, after 3 weeks she had money 2360 pounds.
(ii) 1 year = 52 weeks
6 months = 26 weeks
Amount of money (M) = 2000 + 120n
M = 2000 + 120(26)
M = 5120 pounds
So, after 6 months she had money 5120 pounds.
(iii)
1 1/2 year = 1 year + 6 months
= 52+26
= 78
Amount of money (M) = 2000 + 120n
M = 2000 + 120(78)
M = 11360 pounds
So, after 1 1/2 years she will have 11360 pounds.
Example 2 :
Lars notices that the water in his horse’s drinking trough is only 2 cm deep. The trough is cylindrical. Each time Lars tips a bucket of water into the trough, the water level rises 1.5 cm.
a) Find how much of water level rises if b buckets of water are tipped into the trough.
b) What depth D cm of water is in the trough if b buckets of waters have been emptied into it ?
c) How deep is the water in the trough if lars tips :
(i) 5 buckets (ii) 18 buckets of water into it ?
Solution :
a) Given, the level of water rises 1.5 cm
Here, b is buckets of water
If buckets of water b is tipped into the trough,
So, the level rises b × 1.5 cm
b) Given, the water trough depth is 2 cm
The level rises b × 1.5 cm
If b buckets of water empty, the depth D cm is
So, D = 2 + 1.5b cm
c) (i) 5 buckets
depth (D) = 2 + 1.5b cm
b = 5
D = 2 + 1.5(5)
D = 9.5 cm
So, the depth (D) is 9.5 cm
(ii) 18 buckets of water into it ?
depth (D) = 2 + 1.5b cm
b = 18
D = 2 + 1.5(18)
D = 29 cm
So, the depth (D) is 29 cm.
Example 3 :
Students fill 600 ml bottles from a water cooler containing 50 litres of water.
a) If b bottles are filled, how much water is used ?
b) How much water W liters is left in the cooler if b bottles have been filled ?
c) How much water is left in the cooler if :
(i) 15 bottles (ii) 37 bottles have been filled ?
Solution :
a) Number of bottles filled = b
capacity of each bottle = 600 ml (or) 0.6 liter
Quantity of water used by the students = 0.6b
b) We have 50 liters of water in the cooler, used water is 0.6b liters.
water left in the cooler W = 50 - 0.6b litres
c) (i) 15 bottles
b = 15 bottles
W = 50 - 0.6b litres
= 50 – 0.6(15)
= 50 – 9
= 41 litres
ii) 37 bottles have been filled ?
b = 37 bottles
W = 50 - 0.6b litres
= 50 – 0.6(37)
= 50 – 22.2
= 27.8 litres
Example 4 :
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 minutes
c) 1 hr 15 mins
Solution :
a)
By using given expression, we get
C = 12h+5
C = 12(1)+5
C = 17
So, the cost of hiring a court for $17
b) 30 minutes
1 hr = 60 minutes
30 minutes = 30/60 hr
= 0.5 hr
C = 12h+5
C = 12(0.5)+5
C = 11
So, the cost of hiring a court for $11
c) 1 hr 15 mins
1 hr 15 mins = (1 hr+0.25 hr)
= 1.25 hr
C = 12h+5
C = 12(1.25)+5
C = 20
So, the cost of hiring a court for $20
Example 5 :
The volume of water in a tank t minutes after tap is switched on, is given by
V = 5000 – 20t litres.
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.
By using given expression, we get
When t = 0
V = 5000 – 20t litres
V = 5000 – 20(0)
V = 5000
So, the volume V is 5000 and is the starting volume of water in the tank.
b)
(i) 5 minutes
t = 5 minutes
V = 5000 – 20t litres
= 5000 – 20(5)
= 5000 – 100
V = 4900 litres
(ii) 1 hour
1 hr = 60 mins
t = 60 minutes
V = 5000 – 20t litres
= 5000 – 20(60)
V = 3800 litres
(iii) 3 1/2 hours
3 1/2 hrs = 210 mins
t = 210 minutes
V = 5000 – 20t litres
= 5000 – 20(210)
V = 800 litres
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