Revisions

Introductory Video

Lesson Objectives

❑Writing equations using symbols

❑Problem solving with algebra

❑Measurement problems

❑Money problems

❑Miscellaneous problem solving

Writing equations using symbols

To write equations using symbols;

❑We write each step of the problem using
symbols, taking care to use brackets when
necessary.

❑We can also take algebraic equations and
write them in words or in sentences.

Example 1

Starting with the number 𝑛, rewrite
the following in algebraic form:

a) I think of a number and subtract 5

from it, getting an answer of 16.

b) I think of a number and divide it by
5, getting an answer of 7.

c) I think of a number, add 5, multiply
the result by 3 then add 4. The result is
40.

Example 2

Write the following
equations about the number
𝑛 in English sentences:

a) 𝑛 + 5 = 2

b) 3(𝑛 − 4) = 9

c) 2𝑛 − 5 = 7

d) 3𝑛 + 6 = 21

e) 2(𝑛 + 1) = 16

Problem solving with algebra

The following steps should be followed:

• Step 1: Examine the problem carefully.

• Step 2: Draw a diagram if necessary.

• Step 3: Select a letter or symbol to represent the unknown quantity

to be found.

• Step 4: Set up an equation using the information in the question.

• Step 5: Solve the equation.

• Step 6: Write the answer to the question in a sentence.

• Step 7: Check that your answer satisfies the given conditions.

Example 3

Use equations to solve the following problems:

a) I think of a number, double it, then subtract 5. The result is -6. Find
the number.

b) From twice a certain number, 11 is subtracted, giving a result of 6.
Find the number.

c) When twice a certain number is increased by 3, the result is 37. Find
the number.

d) When one is added to a certain number and the result is halved, 7
results. What is the number?

e) When a number is halved and one is added, the result is 7. What is
the number?

Measurement problems

❑Perimeter

❑Area

❑Volume

❑Angles

Example 4

a) A triangle has sides of length 𝑥 𝑐𝑚, 2𝑥 𝑐𝑚 and
(𝑥 + 3) 𝑐𝑚. Find x given that the perimeter is 23 𝑐𝑚.

b) 4 A rectangle has length 5 cm longer than its
width. Its perimeter is 82 cm. Find the width of the
rectangle.

c) 5 A rectangle has length 3 times its width, and its
perimeter is 36 cm. Find the width of the rectangle.

Money problems

❑When we solve problems involving money, we

need to make sure we use the same units on both
sides of the equation.

Example 5

a) An orange costs twice as much as an apple. The two of them cost a
total of 72 cents. Find the cost of an apple.

b) 2 A TV set costs $100 more than a DVD player. If the two of them
cost a total of $854, find the cost of the TV and DVD player.

c) 3 A handbag costs twice as much as a purse. If Jade buys 2 handbags
and a purse, the total bill is £87.50. Find the cost of the purse.

d) 4 A bowl of noodles costs half as much as a chicken and mushroom
hot pot. If I buy 3 bowls of noodles and 5 hot pots, the total cost is
£ 13.65. Find the cost of one chicken and mushroom hot pot.

Miscellaneous problem solving

❑To solve these problems you should first set up an

algebraic equation.

Classwork

❑Exercise 10a number 1 to 5 page 79

❑Exercise 10b number 1 to 5 page 79

❑Exercise 10c number 1 to 5 page 79

❑Exercise 10d number 1 to 5 page 80

Assignment

❑Exercise 10e number 1 to 8 page 80

❑Exercise 10f number 1 to 8 page 80