Percentage P6 2010 SA2 RGS P2 Q18

There are more pupils in School A than School B. 30% of the pupils in School A is 45 more than 40% of the pupils in School B, If 10% of the pupils in School A leaves to join School B, there will be 200 more pupils in School A than School B. (a) How many pupils are there in School B? (b) How many percent less pupils are there in School B than School A? Leave your answer as fraction in the simplest form.[5 marks][Answer given: 1200, 31 3/7%]


3 A --> 4 B + 45

24 A --> 32 B + 8 x 45 = 32 B + 360


9 A --> 10 B + 1 A + 200

8 A --> 10 B + 200

24 A --> 30 B + 3 x 200 = 30 B + 600


32 B + 360 --> 30 B + 600

2 B --> 600 - 360 = 240

10 B --> 5 x 240 = 1200 pupils

a) It was 1200 pupils.


3 A --> 2 x 240 + 45 = 525

10 A --> 10/3 x 525 = 1750

1750 - 1200 = 550

550/1750 x 100% = 31 3/7%

b) It 31 3/7% less.

Percentage P6 2009 SA1 P2 RGS Q5

5. 2/5 of 80 km is the same as ____ % of 320 km.

2/5 x 80 = 32

32/320 x 100% = 10%

Percentage P6 2009 SA1 P2 RGS Q6

6. Dan and Ella shared a sum of money. When Dan’s share increased from $500 to $605, the amount Ella received decreased by 15%. How much did Ella receive at first? [3]

             100%

[  500  ][         ]

[   605    ][      ]

                85%

15% -- > 605 – 500 = 105

100% -- > 100/15 X 105 = $700

Ella received $700 at first.

Percentage P6 2009 SA1 P2 RGS Q18

18. Container A contains 250 red marbles and 200 blue marbles. Container B contains 600 red marbles and 150 blue marbles. How many red and blue marbles must be moved from Container A to Container B such that 25% of the marbles in Container A are red and 75% of the marbles in Container B are red? [5]

Firstly list out the relationships given.

25 : 75 = 1 : 3              Container A – Red : Blue

75 : 25 = 3 : 1              Container B – Red : Blue

The total number of red marbles and total number of blue marbles remain constant since they are moved from Container A to Container B. (Before = After)

A + 3 B --> 250 + 600 = 850
3 A + B --> 200 + 150 = 350

4 A + 4 B --> 850 + 350 = 1200
1 A + 1 B --> 1200 ÷ 4 = 300

2 B --> 850 - 300 = 550
B --> 550 ÷ 2 = 275
4 B --> 4 x 275 = 1100              There is no need to solve for A.

1100 – 600 – 150 = 350 marbles             
Always remember to write down the unit of measurement.

350 red and blue marbles must be moved from Container A to Container B.

Alternative method 1 – Model Drawing
Firstly list out the relationships given.

250 : 200 = 5 : 4           Container A – Red : Blue (Before)

                                    Not necessary for Container B

                                         

25 : 75 = 1 : 3              Container A – Red : Blue (After)

75 : 25 = 3 : 1              Container B – Red : Blue (After)

Next, move 50 blue marbles (and shaded them) to Container B to achieve the end ratio of 3 : 1. [600 : 150 + 50]

Then shade away 3 units of RA for every 1 unit of BA, until you cannot get any more 3 : 1. [**]

RA [    ][    ] [    ] [    ] [    ]   Cut all units into 2 small units

BA [    ][    ] [    ] [    ]             

After that cut the units into smaller units (in this case – 1 unit into 2 smaller units).

Then repeat ** above, till RA : RB = 1 : 3
[Do you realise that there is no need to draw model for Container B at all]

RA [ ][ ][ ][ ][ ][ ][ ][ ][ ][ ]   250

BA [ ][ ][ ][ ][ ][ ][ ][ ]          200

8 u --> 200

1 u --> 200 ÷ 8 = 25

14 u --> 14 x 25 = 350 marbles

350 red and blue marbles must be moved from Container A to Container B.

Alternative method 2

Firstly list out the relationships given.

250 : 200 = 5 : 4           Container A – Red : Blue (Before)

                                    Not necessary for Container B

                                         

25 : 75 = 1 : 3              Container A – Red : Blue (After)

75 : 25 = 3 : 1              Container B – Red : Blue (After)

Next, move 50 blue marbles (and shaded them) to Container B to achieve the end ratio of 3 : 1.  [600 : 150 + 50]

200 – 50 = 150

Then for Container A, -3 for Red every -1 for Blue (- 3 : - 1) to achieve end results of 1 : 3 for Red : Blue.

As we are finding the number of marbles move, multiply column (Red) by 3 to get same end result of 3 as blue. Then solve.

             Red          Blue

     x 3  ----------------------

750        250          150

- 9         - 3      :     - 1

--------------------------------

  3     :     1      :       3

--------------------------------

750 – 9 u --> 150 – 1 u

8 u --> 750 – 150 = 600

1 u --> 600 ÷ 8 = 75

4 u --> 4 x 75 = 300

Remember to include the 50 blue marbles moved earlier (to make the ratio of the Red to Blue marbles 3 : 1 in Container B.

300 + 50 = 350 marbles

350 red and blue marbles must be moved from Container A to Container B.