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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 October 9th, 2018, 08:06 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 355 Thanks: 1 what is it in the southern hemisphere? The ratio of land and water on our planet is 1 : 2. If this ratio 2 : 3 in the northern hemisphere, what is it in the southern hemisphere? I following this method: In a planet, there are two parts: Northern hemisphere and southern hemisphere. Let total area of planet is 60. (Why we assume 60? Because ratios given, 1+2 = 3 and 2+3 = 5, it should be multiple of this to make calculation easy.) Ratio of land and water on planet = 1:2 So land on planet = (1/3)×60 = 20 Water on planet = (2/3)× 60 = 40 Area of northern hemisphere = area of southern hemisphere = 30 Given, ratio of land and water on north hemi. = 2 : 3 So, land on north.hemi = (2/5)×30 = 12 water on north. Hemi = (3/5)×30 = 18 Ramaining land and water of planet will be on southern hemi. land on south hemi = land on planet – land on north hemi = 20- 12 = 8 water on south hemi = water on planet – water on north hemi = 40 – 18 = 22 Hence ratio is 8:22 i.e. 4:11 Is there any simple solution to solve this one? October 10th, 2018, 04:03 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,632 Thanks: 2080 Using 60 for total area (30 per hemisphere), i.e. land area = 20 and water area = 40, northern hemisphere has land area = 30×2/(2+3) = 12 and water area = 30 - 12 = 18. Hence southern hemisphere has land area = 20 - 12 = 8 and water area = 40 - 18 = 22, and so the land:water ratio for the southern hemisphere is 8:22, which is 4:11. The above is essentially the same as what you did, but given more compactly. I can't find a simpler method. With further compaction, 2 + 1 = 3 and 2(3 + 2) = 10, so rewriting 1:2 as 10:20 and 2:3 as 6:9, the required answer is (10 - 6):(20 - 9), i.e. 4:11. That's effectively the same method, but it's less clear why it works when it's written so compactly. Thanks from Ganesh Ujwal October 12th, 2018, 06:45 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,414 Thanks: 1024 Tags hemisphere, southern Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post paw Calculus 4 April 4th, 2016 07:11 AM john Cartwell Applied Math 0 October 28th, 2014 11:41 AM john Cartwell Calculus 1 October 28th, 2014 11:11 AM jaredbeach Calculus 9 January 12th, 2012 08:49 PM Algebra 2 March 19th, 2009 12:54 PM

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