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

(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

S_n  =  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.

Example 6 :

Twice the sum of length x and width y of the rectangle is the perimeter of rectangle. Write the expression for perimeter.

Solution :

Length be x and width be y.

Sum of length and width = x + y

twice the sum of length and width = 2(x + y)

Example 7 :

You are washing cars for 2 hours. You will receive $6. How much will you earn per hour?

Solution :

Amount earning for 2 hours = $6

Number of hours working = 2 hours

Amount i am earning per hour = Amount i have earned totally ÷ Number of hours working

= 6 ÷ 2

= $3

So, i have earned $3 per hour.

Example 8 :

You have $60. You buy a pair of jeans and a shirt. The pair of jeans costs $27. You come home with $15. How much did you spend on the shirt?

Solution :

Amount i have = $60

Items i have purchased = pair of jeans + a shirt

Cost of pair of jeans = $27

I come with $15

So, 60 can be equated to cost of pair of jeans, cost of a shirt and amount i have remaining.

60 = 27 + cost of shirt + 15

60 = 42 + cost of shirt

Cost of shirt = 60 - 42

= 18

So, cost of a shirt is $18.

Example 9 :

For lunch, you buy 5 sandwiches that cost $3 each. How much do you spend?

Solution :

Number of sandwiches = 5

Cost each sandwich = 3

Amount i spent = 3(5)

= 15

So, $15 is the amount i spent.

Example 10 :

You are running a 4500-foot race. How much farther do you have left to go after running 2000 feet?

Solution :

Distance to be covered in the race = 4500

Distance covered sofar = 2000

Distance to be covered still = 4500 - 2000

= 2500 feet

So, 2500 feet is the distance to be covered yet.

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