Q1. Justina had 72 more Singapore stamps than Malaysia stamps. She gave away some Singapore and Malaysia stamps. The number of Singapore stamps she gave away was 3/4 of the number of Malaysia stamps she had at first. The number of Malaysia stamps she gave away was 1/2 the number of Singapore stamps she had at first. In the end, she had an equal number of each type of stamps, How many Singapore stamps did Justina have at first?questionable_i wrote:Can anyone help me with these questions? in advance.

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Before :

S : 4u + 72

M : 4u

After :

S : 4u + 72 - 3u = 1u + 72

M : 4u - 2u - 36 = 2u - 36

1u + 72 = 2u - 36

1u ------- 108

4u + 72 = 4 x 108 + 72 = 504

Ans : 504 Singapore stamps.

Q2. The number of toys cars Keith had was 1/5 the number of paper aeroplanes. After he gave 1/2 of his paper aeroplanes and 1/3 of his toys cars to his brother, he had 286 more paper aeroplanes than toy cars. (a) How many toy cars did Keith have in the end? (b) How many toy cars and paper aeroplanes did Keith have at first?

(a)

TC : PA

1 : 5

6u : 30u

TC : 6u - 2u = 4u

PA : 30u - 15u = 15u

15u - 4u = 11u ------- 286

1u ------- 286/11 = 26

4u ------- 26 x 4 = 104

(b)

6u + 30u = 36u

36u ------- 36 x 26 = 936

Alternatively,

6u ------- 26 x 6 = 156 (toy cars at first)

30u ------- 26 x 30 = 780 (paper aeroplanes at first)

780 + 156 = 936

Ans : (a) 104 toy cars ; (b) 936 toy cars and paper aeroplanes.

Q3. In a boutique, 40% of the clothing are dresses. 70% of the remainder are skirts and the rest are pants. There are 30 more skirts than dresses. After some dresses are sold, 25% of the remaining clothing in the boutique are dresses. How many dresses are there left in the boutique?

100 - 40 = 60 (remainder)

70% x 60 = 42 (skirts)

60 - 42 = 18 (pants)

42 - 40 = 2

2% ------- 30

1% ------- 30/2 = 15

42% ------- 15 x 42 = 630

18% ------- 15 x 18 = 270

270 + 630 = 900

100% - 25% = 75%

75% ------- 900

1% ------- 900/75 = 12

25% ------- 12 x 25 = 300

Ans : 300 dresses.

Q4.

Image

Area of circle with radius 56cm -------- (22/7) x 56 x 56 = 9856

9856/2.2 = 4480

3.5u x 5u = 17.5u^2

17.5u^2 -------- 4480

u^2 ------- 4480/17.5 = 256

256 = 16 x 16

1u ------- 16

3.5u ------- 16 x 3.5 = 56

5u ------- 16 x 5 = 80

(80 + 56) x 2 = 272

Ans : 272 cm.

Q5. Meng has a total of 1296 black and white buttons. He has 720 more black buttons than white buttons. He puts all the black buttons equally into empty black boxes and puts all the white buttons equally into empty white boxes. There are thrice as many black boxes as white boxes. Each black box contains 4 more buttons than each white box. How many buttons are there in each white box?

1296 - 720 = 576

576/2 = 288 (white)

288 + 720 = 1008 (black)

1008/3 = 336

336 - 288 = 48

48/4 = 12

288/12 = 24

Alternatively,

Total black buttons : 3u ------- (1296 + 720)/2 = 1008

1008/3 = 336

Total white buttons : 1u ------- 1008 - 720 = 288

336 - 288 = 48

48/4 = 12 (number of boxes in 1u)

Number of white buttons in 1 box = 288/12 = 24

Ans : 24 buttons.

Q6. The ratio of Isabellas savings tot Joannas savings was 9 : 8. Isabella and Joanna shared the cost of buying a birthday present for their grandmother in the ratio of 2 : 1 respectively. Isabella used up 2/3 of her savings to pay for her share of the present. Joanna was left with $150 after paying her share. (A) How much was Joanna's savings? (b) What was the cost of the present?

(a)

I : 9u - 2p = 3u = 9u - 6u

2p ------- 6u

1p ------- 3u

J : 8u - 1p = 8u - 3u = 5u

5u ------- 150

1u ------- 150/5 = 30

8u ------- 30 x 8 = 240

(b)

3p ------- 3 x 3u = 3 x 3 x 30 = 270

Ans : (a) $240; (b) $270.