My Math Forum Ratios: Pencils and Notebooks

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 October 4th, 2018, 08:18 PM #1 Newbie   Joined: Oct 2018 From: arizona Posts: 6 Thanks: 0 Ratios: Pencils and Notebooks Suppose p:n = 9:4 then after p-10=n or p=n+10, the ratio 9/4 turns into 4:4 what are the end values of p and n? Last edited by sigma; October 4th, 2018 at 09:02 PM. Reason: More concise wording
 October 5th, 2018, 12:11 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 Your original wording made sense, but was spoilt by your edit. Using p for the number of pencils and n for the number of notebooks, p/n = 9/4 and p - 10 = n. The first equation implies p = 9n/4, and replacing p with 9n/4 in the second equation gives 9n/4 - 10 = n. Hence n = 10/(9/4 - 1) = 8, and so p = 9(8/4) = 18. After 10 pencils are sold, p becomes 8, making p and n each equal 8. The ratio 8:8 is equal to 4:4 (though that could be simplified to 1:1).
 October 5th, 2018, 02:01 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond $$\frac{p}{n}=\frac{9}{4}$$ $$4p=9n$$ $$4p=9(p-10)\Leftarrow n=p-10$$ $$4p=9p-90$$ $$90=5p$$ $$p=18$$ $$\text{end }n=8,\,\text{end }p=8$$

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