John and Jimmy went to the bookshop to purchase some stationaries. The number of pencils John bought was half of the number of pens he bought. On the other hand, Jimmy bought 2/3 as many pencils as pens. If John bought thrice as many pens and pencils as Jimmy, what was the ratio of John’s pens to Jimmy’s pens?
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Pens Pencils Total
John 2u u 3u (pencils John bought was 1/2 of pens he bought)
Jimmy 3p 2p 5p (Jimmy bought 2/3 as many pencils as pens)
3u = 3(5p) = 15p (John bought thrice as many pens and pencils as Jimmy)
u = 5p
<——————————- Pen ————————————–><———Pencil——————->
John [ u ][ u ][ u ]
[ 5p ][ 5p ][ 5p ]
Jimmy [ 3p ][ 2p ]
Hence ratio of John’s pens to Jimmy’s pens = 10p : 3p = 10 : 3
If John bought U pencils, then he bought 2U pens.
If Jimmy bought 2P pencils, then he bought 3P pens.
Given John bought total 3 times total of Jimmy,
John pen to Jimmy pen ratio = 2U/3P = 10P/3P = 10/3 or the ratio is 10: 3
Lol. This looks suspiciously to be “algebra” to me… 🙂
Thank you for the good solution.