
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
September 18th, 2018, 12:03 AM  #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 [1] We know 1/8 of his coins are foreign. [2] 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, 01:38 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,317 Thanks: 1230 
$\ell \text{ is the number of local coins started with}$ $f \text{ is the number of foreign coins started with}$ $n = \ell + f$ after giving away the coins we have $\ell \to \dfrac \ell 2$ $f \to f6$ $\dfrac \ell 2 = (f6) + 71 = f + 65$ $\ell = 2f + 130$ $\dfrac{\ell}{f} = 7$ $\dfrac{2f+130}{f}=7$ $130=5f$ $f = 26$ $\ell = 7f = 182$ $n = 26 + 182 = 208$ 
September 18th, 2018, 01:39 AM  #3 
Senior Member Joined: Apr 2014 From: UK Posts: 895 Thanks: 328 
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 
September 18th, 2018, 02:01 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,302 Thanks: 1974 
If Junhao originally had n coins, ((7/2)/8)n = 71 + (1/8)n  6, so n = 65/((7/2  1)/8) = 208.


Tags 
coin, collection, junhao 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Orthonormal collection  kookie  Linear Algebra  1  November 18th, 2017 08:48 PM 
Ring collection  MathematicallyObtuse  Algebra  5  November 25th, 2010 04:46 AM 
Introduction and keeping a collection  MyNameIsVu  New Users  5  April 19th, 2009 12:28 PM 