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TOPIC EQUATIONS THEORY
03 CONSTRUCTING EQUATIONS
Using equations to solve word problems Example 1
Word problems can be categorised into: The sum of two consecutive numbers is 87.
Find the numbers.
(i) Number Problems Solution
(ii) Measurement Problems Step 1: Underline the keywords that suggest mathematical
(iii) Money Problems operations.
(iv) Age Problems
To solve word problems: Step 2: Select a pronumeral to represent the unknown
quantity.
Step 1: Underline the keywords that suggest
mathematical operations. Let the two consecutive numbers be x and x+1.
Step 2: Select a pronumeral to represent the Step 3: Translate the word problem into an equation.
unknown quantity.
Step 3: Translate the word problem into an equation. The sum of two consecutive numbers = 87
xx++()18= 7
Step 4: Solve the equation.
Step 5: Check that the solution satisfies the given Step 4: Solve the equation.
problem. xx++()18= 7
Step 6: State your answer in words. 21x +=87
28x = 6
The table below shows keywords for addition and x = 43
subtraction. Step 5: Check that the solution satisfies the given problem.
Word Operation Word Operation x = 43
Plus + Minus - x+=1431+=44
Sum + Difference - 43+=44 87
More than + Less than - Step 6: State your answer in words.
Increased + Decreased - The two consecutive numbers are 43 and 44.
by by
Gain + Loss - Example 2
The table below shows keywords for multiplication The sum of two consecutive even numbers is 146.
and division. Find the numbers.
Solution
Word Operation Word Operation Step 1: Underline the keywords that suggest mathematical
Times # Ratio ' operations.
Multiplied # Divided ' Step 2: Select a pronumeral to represent the unknown
by by quantity.
Product of # Quotient of ' Let the two consecutive even numbers be x and
Twice or #2 Half '2 x+2.
double
Triple #3 One-third '3 Step 3: Translate the word problem into an equation.
The sum of two consecutive even numbers = 146
In measurement and money problems, don’t forget to xx++()2 =146
include units in your answer.
Number problems Step 4: Solve the equation.
22x +=146
In number problems, you are required to find an 2x = 144
unknown number given its relationship with the other x = 72
number(s). Step 5: Check that the solution satisfies the given problem.
Number problems could involve The smaller even number: x = 72
(i) Two numbers The next consecutive even number: x+=274.
(ii) Two or three consecutive numbers Step 6 : State your answer in words.
(iii) Two of three consecutive even or odd The two consecutive numbers are 72 and 74.
numbers
TM
YEAR 9 MATHS MAX SERIES VOL.2 22 www.matrix.edu.au
TOPIC EQUATIONS QUESTION
03 CONSTRUCTING EQUATIONS (MEASUREMENT PROBLEMS)
LEVEL NOTES TO STUDENTS
11. A water storage tank is two-thirds full. After 500 litres of 4
water is drained out, the tank is two-fifths full. 3
2
(a) Let the full capacity of the water storage tank be x litres. 1
Write an expression in x for the initial amount of water in
the tank.
(b) Write an equation and solve it to find the capacity of the The amount of water in the tank before and
water storage tank. after draining will be a fraction of x .
12. A truck is loaded with 80 drums. Each drum weighs either 4 Totalweight =
45 kg or 30 kg. The total mass of the 80 drums is 2970 kg. 3 number of drumsw# eightofdrums
2
(a) Let the number of drums weighing 45kg be x. Write 1
an expression in x for the total mass of 45kg drums
and for the total mass of 30 kg drums.
(b) Form an equation and solve it to find the number of The question only asks for the number of
drums weighing 45 kg. drums .
45kg ()x
TM
YEAR 9 MATHS MAX SERIES VOL.2 31 www.matrix.edu.au
YEAR 9 MATHS MAX SERIES VOL.2
CONTENTS
EQUATIONS 01 SOLVING LINEAR EQUATIONS P07
What is a linear eqatin
What es it ean t sle a linear eqatin
Pr ere r slin eqatins
Eqatins ith ne rneral n ne sie
Eqatins ith rnerals n th sies
Eqatins ith ra
ets
Eqatins inlin ra tins
02 REARRANGING EQUATIONS P
Rearranin rla
03 CONSTRUCTING EQUATIONS P22
sin eqatins t sle r rles
er rles
Measreent rles
Mne Prles
Ae Prles
04 INEQUALITIES P
What is an ineqalit
rahin ineqalities n the ner line
Slin linear ineqalities
Slin an rahin ineqalities the r ax##b
Slin an rain ineqalities inlin ra tins
TM
YEAR 9 MATHS MAX SERIES VOL.2 www.matrix.edu.au
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