THREE LINEAR EQUATIONS WITH THREE VARIABLES

Question

A collection of nickels, dimes, and quarters consist of 7 coins with a total of $1.05. If the number of dimes is equal to the number of nickels, find the number of each type of coins. I am still having problems understanding and visualizing the problem enough to break it down in an easy and cohesive manner. What are the linear equations, in order of solving, that lead to the answers? 

Answer 1

x = number of nickels

y = number of dimes

z = number of quarters

 

x + y + z = 7  [total of 7 coins]

0.05x + 0.10y + 0.25z = 1.05  [total money present]

x - y = 0  [number of nickels = number of dimes]

 

These are the 3 equations in 3 unknowns x, y, and z.  Solve for x, y, and z.  I get

 

x = 2 nickels

y = 2 dimes

z = 3 quarters

 

Test the solution.