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****).**

**T****hen 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.