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

 September 17th, 2018, 11:03 PM #1 Member   Joined: Sep 2018 From: Japan Posts: 35 Thanks: 2 Junhao coin collection Junhao has a coin collection. 7/8 of his coins are local coins and the rest are foreign coins. After he gives away 1/2 of his local coins and 6 foreign coins, he has 71 more local coins than foreign coins left. How many coins did he have at first? My work. (I'm not sure how to solve this) Let number of Foreign coins = F Let number of Local coins = L  We know 1/8 of his coins are foreign.  He gives away 1/2 of his local coins and 6 foreign coins, and he has 71 more local coins left: 7/64L + 71 = 1/8F - 6 Note: how I got 7/64L is 7/8 * 1/8 September 18th, 2018, 12:38 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,552 Thanks: 1402 $\ell \text{ is the number of local coins started with}$ $f \text{ is the number of foreign coins started with}$ $n = \ell + f$ after giving away the coins we have $\ell \to \dfrac \ell 2$ $f \to f-6$ $\dfrac \ell 2 = (f-6) + 71 = f + 65$ $\ell = 2f + 130$ $\dfrac{\ell}{f} = 7$ $\dfrac{2f+130}{f}=7$ $130=5f$ $f = 26$ $\ell = 7f = 182$ $n = 26 + 182 = 208$ Thanks from xoritos September 18th, 2018, 12:39 AM #3 Senior Member   Joined: Apr 2014 From: UK Posts: 963 Thanks: 342 7/8 of his coins are local coins and the rest are foreign coins. So, L = 7F After he gives away 1/2 of his local coins and 6 foreign coins, he has 71 more local coins than foreign coins left. So, L/2 = F - 6 + 71 Therefore: 7F/2 = F - 6 + 71 7F = 2F +142 - 12 5F = 130 F = 26 L =182 Total coins he started with was 208 Thanks from xoritos September 18th, 2018, 01:01 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 If Junhao originally had n coins, ((7/2)/8)n = 71 + (1/8)n - 6, so n = 65/((7/2 - 1)/8) = 208. Thanks from xoritos Tags coin, collection, junhao 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 kookie Linear Algebra 1 November 18th, 2017 07:48 PM MathematicallyObtuse Algebra 5 November 25th, 2010 03:46 AM MyNameIsVu New Users 5 April 19th, 2009 11:28 AM

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