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Question

Abi spent of her money on 2 identical bookmarks and some identical pens. The cost of each bookmark to the cost of each pen was 2:3. She bought some more bookmarks with 2/5 of her remaining money and had 24 bookmarks in the end How many pens did she buy at first?

Source: Ang Mo Kio Primary

Answer

Here is how I would do it with block diagrams.

Since the price ratio is 2:3, let’s assume a bookmark cost $2 and a pen cost $3. 

  • The remaining money is bottom 5 blocks.
  • 2/5 of that is two green blocks.
  • Two green blocks are used to pay for 24 – 2 = 22 bookmarks.
  • Each green block is the cost of 11 bookmarks = 2 x 11 = $22.
  • Orange block is cost of 2 bookmarks = $4.
  • Blue block is 22 – 4 = $18.
  • So number of pens bought = $18/$3 = 6.

To be more general, we can say a bookmark costs 2u and a pen cost 3u. But really, a $ is just another unit. So we can use $ itself as the unit. Makes it easier to think about. You can replace the $ above with “u” if you like. 🙂

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                                    Book mark              Pen     

Cost of each                   2u                        3u            Total spent = 1/6 of money

2/5 of remaining money(1-1/6=5/6) = 2/5   x   5/6    =  1/3

1/3 of money   buys (24-2)=   22 bookmarks which is  22 x 2u = $44u

1/6 of money = $44u  /  2  = $22u

Cost of 2 bookmarks = 2 x 2u = 4u

So cost of pens = 22u-4u = 18u

Hence number of pens bought = 18u / 3u =6

 

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Assuming Abi had 6U of money at first.

After spending 1/6 of money or 1U, she was left with 5U

Then she used 2U for 24-2=22 bookmarks

So 1U can buy 11 bookmarks

Cost of a pen was 3/2 times of bookmarks or 1.5 bookmarks

Initially she spent 1U of money and can buy 11 bookmarks

11-2=9

9/1.5=6

So she bought 6 pens initially.

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Edited and reposted. Thank you

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The question seems incomplete. Missing the fraction of money spent, etc. May need to repost.

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