
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 3rd, 2018, 01:35 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  Why did we bring two unknown values x and y?
Wealth tax percentages with remaining taxes like Income tax etc. 2013  1.4% + income tax... 2014 . 1.8% + income tax... If the wealth tax collected in 2013 was 80% of that collected in 2014, the total wealth tax collected in 2013 was approximately what percentage more than that collected in 2014? Solution: Wealth tax = 2013 = (80/100) 2014 2013/2014 = 4/5 2013  wealth tax  1.4% 2014  wealth tax  1.8% (1.4x/1.8y) = (4/5) x/y = 4/5 x 9/7 = 36/35 Percentage more than = 1/35 x 100 = 2.85% Why did we bring two unknown values x and y? Last edited by Ganesh Ujwal; May 3rd, 2018 at 01:39 AM. 
May 3rd, 2018, 03:40 AM  #2 
Senior Member Joined: Feb 2010 Posts: 694 Thanks: 132 
Suppose that today you give me 10%. Now suppose that tomorrow I give you 10%. Are we even?

May 3rd, 2018, 05:01 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,723 Thanks: 1807  Your description was inaccurate (the second occurrence of "wealth tax collected" should have been "wealth taxed"). Let the amount taxed (as distinct from the amount of tax) be x for 2013 and y for 2014 (separate letters for the separate years). The wealth tax collected is then 1.4% of x for 2013, and 1.8% of y for 2014. You are told that 1.4% of x was 80% of 1.8% of y, so 0.014x/(0.018y) = 80% = 4/5, which implies that x/y = 4/5 * 1.8/1.4 = 36/35. 
May 3rd, 2018, 07:32 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 332 Thanks: 1  
May 4th, 2018, 03:57 AM  #5 
Senior Member Joined: Feb 2010 Posts: 694 Thanks: 132  It answers your doubt if you bother to "think". Without the x and y, the 1.4% and 1.8% are meaningless. You must have 1.4% of something. Without any other information you can say 1.4% of x. Now it has meaning. Going back to my example ... you give me 10% today and I give you 10% tomorrow. Are we even? The answer is "it depends". If today you give me 10% of $100 and tomorrow I give you 10% of a half eaten banana, then I don't think you would consider that an even exchange. 

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