ACS Primary 2010 SA1 Math Paper 2 Q18

Keane bought some marbles and gave half of them to Leon. Leon then bought some stamps and gave half of the to Keane. Keane used 5 stamps and Leon gave away 11 marbles. The ratio of the number of stamps to the number of marbles Keane had left then became 1:7 and the ratio of the number of stamps to the number of marbles Leon had left became 1:5. How many stamps did Leon buy?

Solution

M ----- Marbles
S ----- Stamps

Step 1
Keane bought marbles and gave half to Leon,
Keane ----- M
Leon ----- M
Both have same number of marbles.

Step 2
Leon bought stamps and gave half to Keane,
Keane ----- M , S
Leon ----- M , S
Now both have same number of marbles and stamps

Step 3
Keane used 5 stamps, Leon gave away 11 marbles,
Keane ----- M , [S - 5]
Leon ----- [M - 11] , S
Now Keane has 5 stamps less, and Leon 11 marbles less

Step 4
Keane's no. of stamps to no. of marbles now is 1:7,
M ----- (7 units)
[S - 5] ----- (1 unit)
Now Keane has 7 times as many marbles as stamps.

Step 5
Leon's no. of stamps to no. of marbles now is 1:5,
[M - 11] ----- (5 parts)
S ----- (1 part)
Now Leon has 5 times as many stamps as marbles.

Step 6
1 unit of Keane's stamps + 5 ----- 1 part of Leon's stamps
1 unit + 5 ----- 1 part
Keane gave away 5 stamps, so to have an equal no. of stamps as Leon now, we add back the 5 stamps Keane gave away.

Step 7
7 units of Keane's marbles ----- 5 parts of Leon's marbles + 11
7 units ----- 5 parts + 11
Leon gave away 11 marbles, so to have an equal no. of marbles as Keane, we add back the 11 marbles Leon gave away.

Step 8
Comparing marbles with stamps
(Stamps) 1 unit + 5 ----- 1 part (refer to Step 6)
(Marbles) 7 units ----- 5 parts + 11 (refer to Step 7)

Step 9
Multiply stamps by 5
(Stamps) 5 units + 25 ----- 5 parts
(Marbles) 7 units --> 5 parts + 11

(Stamps) 5 units ----- 5 parts - 25
(Marbles) 7 units ----- 5 parts + 11

Step 10
(marbles) - (stamps)
7 units - 5 units --> 5 parts + 11 - 5 parts - (-25)
2 units --> 11 + 25
2 units --> 36
1 unit --> 18

Step 11
1 unit ----- S - 5 (refer to Step 4)
18 ----- S - 5
S ----- 18 + 5 = 23
This is the no. of stamps Leon had after giving half away.

Step 12
Leon bought,
2 x 23 = 46

Answer: 46 stamps

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ACS Primary 2010 SA1 Math Paper 2 Q17

The shaded figure below is formed by semicircles, quarter circles and straight lines of 15 cm each. For each of the following, use the calculator value of to find
a) the perimeter of the shaded figure, correct to 2 decimal places.
b) the area of the shaded figure, correct to 2 decimal places.

Solution

(a)
Circumference of 2 semicircles (1 circle)
--> 2r
= 2 x 7.5cm
= 47.12 cm

Circumference of 2 quarter circles (1 semi circle)
-->()2r
= ()(2)() x 15cm
= 47.12 cm

Length of vertical line on the left side of figure
--> 2 x 15cm = 30cm


Perimeter of shaded figure
--> 47.12cm + 47.12cm + 30cm
= 124.25cm

Answer: 124.25 cm


(b)
Area of 2 quarter circles (1 semi circle)
-->()
= () x 15cm x 15cm
= 353.43


Area of 2 semi circles (1 circle)
-->
= x 7.5cm x 7.5 cm
= 176.71

Area of whole figure
--> 30cm x 30cm
= 900

Shaded area
--> 900 - 353.43 - 176.71
= 369.86

Answer: 369.86

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