from PSLE

[Jenny]

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?

No official answer, this was posted at the yahoo group (don't look there if you want to figure it out on your own), my answer is 68 (I solved it a little different than there).

[Mary P]

Very interesting and challenging problem, Jenny. Is the PSLE an exit exam for primary level in Singapore? Usually I can come up with a solution eventually, but these students have time constraints, don't they?

I will post my solution, IF others will also give us their various methods. I get to do these problems frequently so, ... perhaps someone else would like to start??

[Jenny]

The person who posted it at the yahoo site claims it was on that test this year, and complained that it was too hard to be on such a test.

[Mary P]

Does anyone have a solution? I will post one possible solution by the weekend if anyone is curious but stuck. I would like to see other solutions besides mine.

[lady.grae]

Well, it's definitely a challenge, but it doesn't require anything that isn't taught by the end of 6B. I started with bars, then switched to a little algebraic representation, but only because I didn't want to deal with the pain of drawing the bars for each boy scaled to each other. Just a little substitution after that.

I didn't do CWP 6 with any of my students, but this one seems to be about on par with the most difficult of the CWP 5 problems.

[Mary P]

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did Ken buy?
Jim
|--------------------------C-------------------------||-------------------------C-------------------------|
Ken
|------S-----||------S-----|

Both Jim and Ken give each other half of their goodies. Now they have an equal number of sweets, an equal number of chocolates, and an equal number of total goodies. Both Jim and Ken’s bars look like the following:
|------S------||--------------------------C-------------------------------|

Jim eats 12 sweets and the remainder of the goodies is in the ratio 1:7.
|------S------||----------------------------C-------------------------------|
|//12//|---o--||---o---||---o---||---o---||---o---||---o---||---o---||--o---|

Ken eats 18 chocolates and the remainder of the goodies is in the ratio 1:4.
|------S-----||----------------------------------C--------------------------|
|------x-----||------x-----||------x-----||------x-----||-----x-----|///18///|

Jim’s sweets before eating = Ken’s sweets before eating
|//12//|---o--|
|-------x-----|

Jim’s chocolates before eating = Ken’s chocolates before eating. Also make the following substitution: |//12//|---o--| is the same as |-------x-----|
|--o---||---o---||---o--||---o---||---o---||---o--||---o---|
|------x-----||------x-----||------x-----||------x----|//18/|
|//12/|---o--|//12/|---o---|//12/|---o---|//12//|-o--|//18//|

Compare the first and third bars, reordering the third bar.
|---o---||---o---||---o---||---o---||---o---||---o---||---o---|
|---o-- ||- --o-- ||---o---||---o----|///////////66////////////////|

3 |---o-- | units = 66
One |---o-- | unit = 22
One S unit = |//12//|---o--|
= 22 + 12
= 34
Ken originally had 2 S units = 68 sweets ☺

[Evelyn]

I hope you guys can understand.
That's the way i taught my DD.

[Candid]

Eveyln I don't know about the math, but boy I love that graphic.