EVALUATING ALGEBRAIC EXPRESSIONS WORD PROBLEMS

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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