77
CHAPTER 11
PROBLEM SOLVING
AIM: At the end of this section the student must be able to:
S apply the different problem solving techniques to solve various problems
S use variables to write a number sentence
S use inspection to solve equations
S solve equations by using equation laws
11.1 DIFFERENT TECHNIQUES
Problem solving relates to everyday situations. Like the amount of money payable for articles
bought, total distance travelled per day by a representative and age of a person years ago.
The first step in solving any problem, is to read carefully and to make sure you understand what
you are being asked to find out! Read through an exercise twice or even three times before trying
to solve it.
We are going to look at some problem solving techniques.
11.1.1 Substitute the wanted solution with 9
EXAMPLE 11.1
This a menu for Quick-serve Ice-cream shop:
MENU
Ice-cream cone ............................R1,50
With Flake........................R1,90
With nuts..........................R1,80
With nuts and flake...........R2.20
Ice-cream tub...............................R1,60
With nuts..........................R1,90
Cold drink..................................... 95c
Milk shake....................................R2,25
1. What is the price of an ice-cream cone with flake and a cold drink?
2. How many ice-cream cones can be bought for R10?
3. How much change will you get?
4. You buy two ice-cream cones with flake and nuts, one ice-cream tub without nuts and
three milkshakes. What are you going to pay?
, 78
In each case, we are going to substitute the wanted solution with the symbol 9 .
1. The price of one ice-cream cone with flake is R1,90 and the price of one cold drink is 95c.
So: Ice-cream cone with flake + cold drink :
R1,90 + R0,95 = 9
(Remember to make cents rands!)
R1,90 + R0,95 = R2,85
The price of an ice-cream cone with flake and a cold drink is R2,85.
2. The price of one ice-cream cone is R1,50, so for R10 you can buy:
R1.50 * 9 = R10,00
R1.50 * 6 = R9.00, so you can buy 9 cones for R10. ( 7 * R1,50 gives
R10,50, which is more then R10.)
3. The price you must pay is R9,00. Change will then be:
R10,00 - R9,00 = 9
R10,00 - R9,00 = R1,00
4. The price of one ice-cream cone with flake and nuts is R2,20, of one tub without nuts
R1,60 and of one milkshake R2,25. The price to be paid is:
2 * R2,20 + R1,60 + 3 * R2,25 = 9
2 * R2,20 + R1,60 + 3 * R2,25 = R12,75
11.1.2 Use a table.
EXAMPLE 11.2
The Love-Travel family decides to visit their
relatives.
CHAPTER 11
PROBLEM SOLVING
AIM: At the end of this section the student must be able to:
S apply the different problem solving techniques to solve various problems
S use variables to write a number sentence
S use inspection to solve equations
S solve equations by using equation laws
11.1 DIFFERENT TECHNIQUES
Problem solving relates to everyday situations. Like the amount of money payable for articles
bought, total distance travelled per day by a representative and age of a person years ago.
The first step in solving any problem, is to read carefully and to make sure you understand what
you are being asked to find out! Read through an exercise twice or even three times before trying
to solve it.
We are going to look at some problem solving techniques.
11.1.1 Substitute the wanted solution with 9
EXAMPLE 11.1
This a menu for Quick-serve Ice-cream shop:
MENU
Ice-cream cone ............................R1,50
With Flake........................R1,90
With nuts..........................R1,80
With nuts and flake...........R2.20
Ice-cream tub...............................R1,60
With nuts..........................R1,90
Cold drink..................................... 95c
Milk shake....................................R2,25
1. What is the price of an ice-cream cone with flake and a cold drink?
2. How many ice-cream cones can be bought for R10?
3. How much change will you get?
4. You buy two ice-cream cones with flake and nuts, one ice-cream tub without nuts and
three milkshakes. What are you going to pay?
, 78
In each case, we are going to substitute the wanted solution with the symbol 9 .
1. The price of one ice-cream cone with flake is R1,90 and the price of one cold drink is 95c.
So: Ice-cream cone with flake + cold drink :
R1,90 + R0,95 = 9
(Remember to make cents rands!)
R1,90 + R0,95 = R2,85
The price of an ice-cream cone with flake and a cold drink is R2,85.
2. The price of one ice-cream cone is R1,50, so for R10 you can buy:
R1.50 * 9 = R10,00
R1.50 * 6 = R9.00, so you can buy 9 cones for R10. ( 7 * R1,50 gives
R10,50, which is more then R10.)
3. The price you must pay is R9,00. Change will then be:
R10,00 - R9,00 = 9
R10,00 - R9,00 = R1,00
4. The price of one ice-cream cone with flake and nuts is R2,20, of one tub without nuts
R1,60 and of one milkshake R2,25. The price to be paid is:
2 * R2,20 + R1,60 + 3 * R2,25 = 9
2 * R2,20 + R1,60 + 3 * R2,25 = R12,75
11.1.2 Use a table.
EXAMPLE 11.2
The Love-Travel family decides to visit their
relatives.
