WORD PROBLEMS ON EVALUATING ALGEBRAIC EXPRESSIONS

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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