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October 4th, 2018, 09:18 PM  #1 
Newbie Joined: Oct 2018 From: arizona Posts: 2 Thanks: 0  Ratios: Pencils and Notebooks
Suppose p:n = 9:4 then after p10=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 10:02 PM. Reason: More concise wording 
October 5th, 2018, 01:11 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,950 Thanks: 1842 
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, 03:01 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,884 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
$$\frac{p}{n}=\frac{9}{4}$$ $$4p=9n$$ $$4p=9(p10)\Leftarrow n=p10$$ $$4p=9p90$$ $$90=5p$$ $$p=18$$ $$\text{end }n=8,\,\text{end }p=8$$ 

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notebooks, pencils, ratio, ratios 
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