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 By: mlteo (offline)  Monday, June 04 2012 @ 10:23 PM CDT (Read 1788 times)
mlteo

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

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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