Q&A - PSLE Math

[alfretztay]

The ratio of cats to dogs in a shelter was 7:10 in January. In Febuary, 20 dogs were adopted from the shelter and 32 cats were found by the shelter. The ratio of cats to dogs becomes 22:15 now. Find the number of cats and number of dogs in January.

For cats :
7u + 32 -> 22p
70u + 320 -> 220p

For dogs :
10u - 20 -> 15p
70u - 140 -> 105p

115p -> 460
1p -> 4
10u - 20 -> 15 x 4 = 60
10u -> 80
1u -> 8
7u -> 56 (cats)
10u -> 80 (dogs)

Ans : 56 cats and 80 dogs.

[alfretztay]

Mary bought some red marbles and gave half to Kate.
Kate bought some blue marbles and gave half to Mary.
Mary lost 16 red marbles and Kate lost 55 blue marbles.
The ratio of Mary's red marbles to blue marbles became 18:85.
The ratio of Kate's red marbles to blue marbles became 7:20.
How many red marbles did Mary buy?

For Mary :
Red -> 10u - 5u - 16 = 5u - 16
Blue -> 5p
(5u - 16) x 85 -> 5p x 18
425u - 1360 -> 90p
14875u - 47600 -> 3150p


For Kate :
Red -> 5u
Blue -> 10p - 5p - 55 = 5p - 55
(5p - 55) x 7 = 5u x 20
35p - 385 -> 100u
100u + 385 -> 35p
9000 + 34650 -> 3150p

5875u -> 82250
1u -> 14
10u -> 140

Ans : 140 red marbles

[EC72]

[EC72]

Mary bought some red marbles and gave half to Kate.
Kate bought some blue marbles and gave half to Mary.
Mary lost 16 red marbles and Kate lost 55 blue marbles.
The ratio of Mary's red marbles to blue marbles became 18:85.
The ratio of Kate's red marbles to blue marbles became 7:20.
How many red marbles did Mary buy?

For Mary :
Red -> 10u - 5u - 16 = 5u - 16
Blue -> 5p
(5u - 16) x 85 -> 5p x 18
425u - 1360 -> 90p
14875u - 47600 -> 3150p


For Kate :
Red -> 5u
Blue -> 10p - 5p - 55 = 5p - 55
(5p - 55) x 7 = 5u x 20
35p - 385 -> 100u
100u + 385 -> 35p
9000 + 34650 -> 3150p

5875u -> 82250
1u -> 14
10u -> 140

Ans : 140 red marbles

I am confused. Can you please explain to me this following part... Thank you.

(5u - 16) x 85 -> 5p x 18 ----> why isn't it (5u - 16) x 18 -> 5p x 85
(5p - 55) x 7 = 5u x 20 ----> why isn't it (5p - 55) x 20 = 5u x 7

[alfretztay]

Mary bought some red marbles and gave half to Kate.
Kate bought some blue marbles and gave half to Mary.
Mary lost 16 red marbles and Kate lost 55 blue marbles.
The ratio of Mary's red marbles to blue marbles became 18:85.
The ratio of Kate's red marbles to blue marbles became 7:20.
How many red marbles did Mary buy?

For Mary :
Red -> 10u - 5u - 16 = 5u - 16
Blue -> 5p
(5u - 16) x 85 -> 5p x 18
425u - 1360 -> 90p
14875u - 47600 -> 3150p


For Kate :
Red -> 5u
Blue -> 10p - 5p - 55 = 5p - 55
(5p - 55) x 7 = 5u x 20
35p - 385 -> 100u
100u + 385 -> 35p
9000 + 34650 -> 3150p

5875u -> 82250
1u -> 14
10u -> 140

Ans : 140 red marbles

I am confused. Can you please explain to me this following part... Thank you.

(5u - 16) x 85 -> 5p x 18 ----> why isn't it (5u - 16) x 18 -> 5p x 85
(5p - 55) x 7 = 5u x 20 ----> why isn't it (5p - 55) x 20 = 5u x 7

Let me just use "For Mary : Red -> 10u - 5u - 16 = 5u - 16. Blue -> 5p" as that for Kate's is the same.
From "The ratio of Mary's red marbles to blue marbles became 18:85" it means
5u - 16 : 5p = 18 : 85
I believe that it may be more difficult to understand for some when it is written in terms of ratio.
So I shall write the above in fractions, equivalent fractions that is.
5u - 16/18 = 5p/85
When cross-multiplied, one will arrive at (5u - 16) x 85 -> 5p x 18.

I will then use very simple fractions to drive home the point as follows :
1/2 = 2/4
1 x 4 = 2 x 2
or
to avoid confusion caused by the same number 2,
2/3 = 4/6
2 x 6 = 3 x 4
I hope I have adequately helped clear your confusion and aided you in your understanding.

[EC72]

very much alfretztay for your detailed explanation. Understand it more clearly now.

[numeric]

Anyone can help please?


Mary and June took part in a cycling race. Both of them cycled at a constant speed throughout the race. Mary cycled at a speed of 24km/h. When June was half way through the race, Mary was 4 km in front of her. Mary reached the finishing line at 11am. At what time did June reach the finishing line?

Constant speed -> When distance doubles, time duration doubles.

Halfway during June’s run: June is 4km behind Mary -> June is 4/24 h = 10min behind Mary.
Completion of June’s run (double the distance): June is 2*10min behind Mary.

Hence June reached the finishing line at 11:20am.

[Jerico]

Hi, Can someone please help with this question ? Tks in adv !

[Jerico]

Hi, Can someone please help with this question ? Tks in adv !

[sushi88]

Hi, Can someone please help with this question ? Tks in adv !

This is essentially a large circle of radius 28 cm with 2 smaller circles inside it with radius 14cm.
Area of shaded area
= area of large circle - area of 2 small circles
= pi(28)(28) - 2pi(14)(14)
= pi(784-392)
= 392pi cm2

Perimeter of one shaded region
= Perimeter of quadrant + perimeter of semi-circle
= 2pi(28)/4 + 2pi(14)/2
= 28pi cm

Perimeter of 4 shaded region
= 4 x 28pi
= 112pi cm