A group of painters is painting the classrooms. If they paint 6 classrooms per day, they will be able to complete 1 day ahead of schedule. If they paint 4 classrooms per day, they will be 2 days behind schedule. How many classrooms are there?

6 x 1 (1 day earlier)

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[ ][ ][ ][ ][ ][ ]

[ ][ ][ ][ ] |

| |Number of classrooms

4 x 2 (need 2 more days)

2 u --> 4 x 2 + 6 x 1 = 14

1 u --> 14 / 2 = 7 days

7 - 1 = 6

6 x 6 = 36 classrooms

[or 7 + 2 = 9

9 x 4 = 36 classrooms]

There were 36 classrooms.

## Friday, December 31, 2010

### Decimal P6 2010 Pei Hwa CA1 Q18

7 apples cost $4.00.

9 oranges cost $11.00.

James bought a total of 1000 apples and oranges for $999.00.

How many apples and how many oranges did he buy?

7 A + 9 O --> 1000

4 A + 11 O --> 999

28 A + 36 O --> 4 x 1000 = 4000

28 A + 77 O --> 7 x 999 = 6993

41 O --> 6993 - 4000 = 2993

9 O --> 9/41 x 2993 = 657 oranges

7 A --> 1000 - 657 = 343 apples

He bought 343 apples and 657 oranges.

9 oranges cost $11.00.

James bought a total of 1000 apples and oranges for $999.00.

How many apples and how many oranges did he buy?

7 A + 9 O --> 1000

**Use 7 A and 9 O for the number of apples and oranges respectively to avoid handling fractions or decimals**4 A + 11 O --> 999

28 A + 36 O --> 4 x 1000 = 4000

28 A + 77 O --> 7 x 999 = 6993

41 O --> 6993 - 4000 = 2993

9 O --> 9/41 x 2993 = 657 oranges

7 A --> 1000 - 657 = 343 apples

He bought 343 apples and 657 oranges.

## Thursday, December 30, 2010

### Percentage P6

In a primary school, 50 pupils were surveyed on the pets they liked. 80% of the pupils liked dogs, 50% of them liked birds and 34% of them liked rabbits. The survey results were that 1 out of every 5 pupils did not like any of the animals. What is the least number of pupils who liked all 3 types of animals. [Ans : 2]

1/5 x 50 =10 -- did not like pets

100% --> 50

80% --> 80/100 x 50 = 40 -- like dogs

50% --> 50/100 x 50 = 25 -- like birds

34% --> 34/100 x 50 = 17 -- like rabbits

25 + 17 - 40 = 2 pupils

The least number of pupils who liked all 3 types of animals is 2.

1/5 x 50 =10 -- did not like pets

100% --> 50

80% --> 80/100 x 50 = 40 -- like dogs

50% --> 50/100 x 50 = 25 -- like birds

34% --> 34/100 x 50 = 17 -- like rabbits

25 + 17 - 40 = 2 pupils

**Least overlap between those who like birds and rabbits**The least number of pupils who liked all 3 types of animals is 2.

### Whole Number P6

Wilson purchased a certain number of wallets at $6 each. If he had purchased those at $8 each, he would have purchased 20 fewer wallets. How much money did he have? [Ans : $480]

6 : 8 = 3 : 4

1 u --> 20

4 u --> 4 x 20 = 80

6 x 80 = $480

He had $480.

6 : 8 = 3 : 4

**Ratio of the number is inversely proportional to the price**1 u --> 20

4 u --> 4 x 20 = 80

**Note: 4 u at $6 (3 u at $8) [inverse proportion]**6 x 80 = $480

He had $480.

### Percentage P6

Benny spent 15% of his salary on food and $440 on camera. Then he spent 30% of the remainder on clothes and saved the rest of his salary. He found that the amount he spent on clothes was $120 more than the amount he had spent on food.

(a) How much did he spend on food? Ans: $360

(b) How much did he save? Ans: $1120

30% r --> 15% + $120

70/30 x 15% = 35%

70/30 x 120 = $280

70% r --> 35% + $280

100% - 15% - 15% - 35% = 35%

35% --> 440 + 120 + 280 = $840

15% --> 15/35 x 840 = $360

a) He spent $360 on food.

840 + 280 = $1120

b) He saved $1120.

(a) How much did he spend on food? Ans: $360

(b) How much did he save? Ans: $1120

30% r --> 15% + $120

70/30 x 15% = 35%

70/30 x 120 = $280

70% r --> 35% + $280

100% - 15% - 15% - 35% = 35%

35% --> 440 + 120 + 280 = $840

15% --> 15/35 x 840 = $360

a) He spent $360 on food.

840 + 280 = $1120

b) He saved $1120.

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