S sigma Oct 2018 7 0 arizona Oct 4, 2018 #1 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: Oct 4, 2018

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?

skipjack Forum Staff Dec 2006 21,387 2,410 Oct 5, 2018 #2 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).

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).

greg1313 Forum Staff Oct 2008 8,008 1,174 London, Ontario, Canada - The Forest City Oct 5, 2018 #3 $$\frac{p}{n}=\frac{9}{4}$$ $$4p=9n$$ $$4p=9(p-10)\Leftarrow n=p-10$$ $$4p=9p-90$$ $$90=5p$$ $$p=18$$ $$\text{end }n=8,\,\text{end }p=8$$

$$\frac{p}{n}=\frac{9}{4}$$ $$4p=9n$$ $$4p=9(p-10)\Leftarrow n=p-10$$ $$4p=9p-90$$ $$90=5p$$ $$p=18$$ $$\text{end }n=8,\,\text{end }p=8$$