**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**

## 4 comments:

2x36 is not 46...

2x36=72

It should be

2 x 23= 46Not 2 x 36

Mistake corrected.

Thanks for highlighting it.

Hi, the posted solution is unacceptably long! There is a much shorter one!

There are many ways to solve PSLE Math problems. The above illustration is long because every step is explained in detail.

Shorter methods are more elegant but they do not help weaker students understand how the problem is solved.

The purpose of this blog is to help weaker students and hence, the more detailed and longer explanation type method is used.

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