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 By: mlteo (offline)  Monday, June 04 2012 @ 10:23 PM CDT (Read 1733 times)
mlteo

Please give your solution to this question

1.Keane bought some marbles and gave half of them to Leon. Leon
bought some stamps and have half of them 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?

Thanks.

Newbie

Registered: 12/31/06
Posts: 10

 By: awyw1201 (offline)  Tuesday, June 05 2012 @ 02:12 AM CDT
awyw1201

Quote by: mlteo

Please give your solution to this question

1.Keane bought some marbles and gave half of them to Leon. Leon
bought some stamps and have half of them 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?

Thanks.

Is this a PSLE 5 yr series question? Thought it look familiar.

Here's the solution:

Use units and parts.

Keane----S:M = 1u:7u
Leon----S:M = 1p:5p

Since Keane bought only marbles and he gave half to Leon, this implies that
7u = 5p +11---(1)

Since Leon bought only stamps and gave half to Keane, this means that
1p = 1u + 5 ---(2)

(2) x 5-----5p = 5u + 25---(3)

Substitute (3) into (1), we have
7u = 5u + 25 +11
2u = 36
1u =18
No. of stamps Leon bought---- 2x (18 +5) = 46

Ans: 46 stamps

Regular Member

Registered: 07/08/11
Posts: 87

 By: echeewh (offline)  Tuesday, June 05 2012 @ 03:03 AM CDT
echeewh

Hey there,

Following pls find the worked solution:

<Before>
NUmber of Marbles(M) K, L had is same (1:1)
NUmber of Stamps(S) K, L had is same (1:1)

<Process>
K used 5S; L gave away 11M;

<After>
KS : KM
1 : 7

LS : LM
1 : 5

K's model:
Working backwards and since K used 5S and K's number of Marbles (M) remains unchanged, we have ...
(***- used to bufferup whitespace - imagine these are all white spaces)

*******5
KS |--|-|
KM |--|--|--|--|--|--|--|

KS: 1u + 5
KM: 7u

L's model:
Since number of Stamps (S) L had in the end remains the same as Before and LS : LM is 1:5, we have ...

LS |--|-|
LM |--|-|--|-|--|-|--|-|--|-|

LS: 1u + 5
LM: 5u + 25

In the process, L gave away 11M. Since L had same number of Marbles (M) as K at the beginning (i.e. 7u), we have ... (also comparing KM and LM models above)

7u - 5u - 25 --> 11
2u --> 11 + 25 = 36
1u --> 18

LS <Before> = 1u + 5 --> 18 + 5 = 23

Referring to <Before> model in which number of Stamps (S) K and L had are the same, we have ...

LS Bought = 2 x 23 = 46

====================================

Trust the above helps.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 By: mlteo (offline)  Tuesday, June 05 2012 @ 03:29 AM CDT
mlteo

Thank you so much to both.

Newbie

Registered: 12/31/06
Posts: 10

 By: mlteo (offline)  Tuesday, June 05 2012 @ 03:39 AM CDT
mlteo

Thank you so much to both.

Newbie

Registered: 12/31/06
Posts: 10

 By: mlteo (offline)  Tuesday, June 05 2012 @ 03:46 AM CDT
mlteo

Thank you so much to both.

Newbie

Registered: 12/31/06
Posts: 10

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