ARM introduction 2013 09-09

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Mrs Li bought 1.6Kg of red and green beans. 30% of the beans were green. After Mrs Li used some of the green beans to make a dessert, only 20% of the beans left were green. How much green beans did Mrs Li use? red green 1.6Kg 3/10 1/5 -? X 7u 3u 4p 1p x 4=28u x 4=12u x7=28u x7=7u 28u+12u 1600 40u1600 1u1600/40=40 12u-7u 5u 5u5x40=200g (ans.) Note: External Unchanged / Single Unchanged

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The ratio of Jane's money to Mary's money was 3:4 at first. After Jane gave Mary $24, the ratio of Jane's money to Mary's money became 1:2. What was the total amount of money they had altogether? Jane Mary + 24 4u 2p 9u-7u 24 2u24 1u24/2=12 21u 21x12=252 (ans.) Note: Total Unchanged / Internal Transfer -24 1 p 3u 7u 3p X3 =21u X7 =21u x7=7u x7=14u x3=9u x3=12u

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Alla is 2/3 as old as Bebe . In 15 years' time, A lla will be 5/6 of Bebe's age How old is A lla now? Alla Bebe +15 3 u 6 p 5u-2u 15 3 u15 1u15/3=5 2 u 2x5=10 (ans.) Note: Constant Difference / Difference Unchanged +15 5p 2 u 1u 1p X1=1u X1=5u X1=6u

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At first, Judy had thrice as much money as her brother. After her mother had given $35 to her and $45 to her brother, Judy had twice as much money as her brother. How much money did Judy have at first? Judy brother +45 1u 1p 2p3u+35 1p 1u+45 Note: External Changed / Total Change / All Changing +35 2 p 3u 2 p 2u+90 x2 3u+35=2u+90 3u 35 2 u 90 3u-2u 90-35 1u55 3u 3x55=165 (ans.)

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If Melvin gives $15 to Ramesh , he will have thrice as much money as Ramesh . If Ramesh gives $35 to Melvin, Melvin will have four times as much money as Ramesh . How much money does Melvin have? Melvin Ramesh +15 1u Note: Gap & Difference / Case 1 Case 2 -15 3 u 15u+15 C1 -35 4u+35 1p +35 4p C2 Melvin Ramesh 4u 5 p X5=20u X5=15u X5=5u X4=20u X4=16u X4=4u 4u+35 Note: Total Unchanged / Internal Transfer 4u+35+15=5u 5u-4u  35+15 1u 50 15u+15 15x50+15=765 (ans.)

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Johnny had the exact amount of money to buy 5 mangoes and 8 oranges. If he were to buy 8 mangoes and 5 oranges instead, he would be short of $6. If a mango costs $4, how much money did Johnny have? Note: Excess & Shortage / Gap & Difference Total amount ($) 5x4=$20 $20 8 OR 8 x4=$32 $32 5 OR $6 8 OR – 5 OR  32-6-20 3 OR  6 1 OR 2 8 OR +20 8x2+20=$36 (ans.)

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Owen has 20% more marbles than Danny. Danny has 40% less marbles than Connie. Owen has 21 marbles less than Connie. How many marbles does Danny have? Note: Repeated Identity 1/5 2/5 Owen Danny Connie 3p 5u 6u 5p X3=15u X3=18u X5=25u X5=15u 21 25u-18u 21 7u21 1u21/7=3 15u 15x3=45 (ans.)

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1/4 of Alan's salary is equal to 2/5 of his sister's salary. When his sister increase her savings by $123 and Alan spent $165, they have an equal amount of money in their savings. (a) How much money did his sister have finally? (b) How much money did Alan have at first? Note: Equal S tage / Equal Concept 2/8 Alan sister 8u 5u -165 +123 1p 1p 8u-165=5u+123 5u+123 5x96+123=603 (a) 8u 8x96=768 (b) 1p 8u-165 1p 5u+123 8u-5u 123+165 3u288 1u288/3=96

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The cost of 1 table and 1 stool is $397. The cost of 2 chairs and 1 table is $721. The total cost of 5 chairs,2 tables and 3 stools is $1856. Find the cost of 1 chair. Note: Simultaneous / Two Variables Table Stool Chair $ 1 1 397 1 2 721 2 3 5 1856 1+1+2=4 1+0+3=4 0+2+5=7 397+721+1856=2974 1x4=4 1x4=4 0x4=0 397x4=1588 4-4=0 4-4=0 7-0=7 2974-1588=1386 7/7=1 1386/7=198 (ans.)

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In a wallet, there is a total value of $295 of $2-notes, $5-notes and $10-notes. There are twice as many $10-notes as $2-notes. The value of the $5-notes is $55 more than that of $2-notes. Find the ratio of the number of $2-notes to the number of $5-notes to the number of $10-notes. Note: Number x Value Number Each Total $2-notes $5-notes $10-notes 295 1u 2u 2 5 10 1ux2=2u 2u+55 2ux10=20u 2u+2u+55+20u 295 2u+552x10+55=75 75/5=15 15 (10) (20) 10:15:20 (75) x = 2u+2u+20u295-55 24u240 1u240/24=10 2:3:4 (ans.)

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