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Friday, October 3, 2014

Word Problem - Coin Problem

Category: Algebra

"Published in Vacaville, California, USA"

A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $ 2.75, how many dimes and how many quarters does he have?

Solution:

From the description of a given word problem, it is an application of linear equation with two equations, two unknowns.  

Let x = be the number of dimes or 10 cent coins
      y = be the number of quarters or 25 cent coins
 
From the statement "A man has 14 coins in his pocket, all of which are dimes and quarters.", then the working equation is


From the statement "If the total value of his change is $ 2.75,..", then the working equation is

  
Hence, the working equations for the given problem are



From the first equation,



Substitute the value of y to the second equation, we have







Substitute the value of x to any of two equations, we have





Therefore, there are 5 coins of dime and 9 coins of quarter in his pocket. 

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