130x Filetype PDF File size 0.44 MB Source: bookshop.matrix.edu.au
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
no reviews yet
Please Login to review.