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

 August 2nd, 2019, 10:05 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 476 Thanks: 1 Solve this two doubts in mixture problem. A can contains a mixture of two liquids A & B in the ratio 7:5 When 9 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. Liters of liquid A contained by the can intially was? Solution: A:B Ratio 7:5 A:B = 7:9 4===9 16===36*7/12=21 How 4 corresponds to 9? Why 4 is multiplied both sides to get 16 & 36 in last step? August 2nd, 2019, 01:14 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 The 7:5 ratio represents 7(9/4)L:5(9/4)L, which total 12(9/4)L. (The 9/4 comes from 9/(9 - 5).) To get the original volumes, one scales up by (12(9/4) + 9)/(12(9/4)), which is 4/3. Hence the original volume of A was 7(9/4)(4/3)L = 7(36/12)L = 21L. The above explains everything except the "16" in the last line of the solution. I'm not sure why it's there. August 2nd, 2019, 08:09 PM   #3
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Quote:
 Originally Posted by skipjack The 7:5 ratio represents 7(9/4)L:5(9/4)L
How 9/4 came? August 3rd, 2019, 04:38 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 The 9 is because 9L of liquid B are added. The 4 is because the A:B ratio changes from 7:5 to 7:9 and 9 - 5 = 4. Multiplying both numbers in the ratio by 9/4 doesn't change the ratio, but changes the increase in the second value from 4 to 9. The numbers used for the ratio have therefore become the numbers of Liters of liquids A and B. August 4th, 2019, 03:16 AM   #5
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Quote:
 Originally Posted by skipjack The numbers used for the ratio have therefore become the numbers of Liters of liquids A and B.
How numbers in ratio become the number of liters of Liquids A & B? August 4th, 2019, 10:55 AM #6 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 The 7:5 ratio becomes written as (63/4):(45/4). The 7:9 ratio becomes written as (63/4):(81/4). Now 45/4 + 9 = 81/4, and clearly any factor other than 9/4 wouldn't achieve that. Hence (63/4)L and (45/4)L are the volumes immediately prior to 9L of liquid B being added. Tags doubts, mixture, problem, solve 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 Ganesh Ujwal Number Theory 3 May 3rd, 2018 03:26 AM Kimmysmiles0 Algebra 2 April 4th, 2012 07:38 PM weeweewee Algebra 1 January 6th, 2012 01:51 AM Horizont Algebra 3 September 16th, 2008 10:12 AM

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