Let number of nickels, dimes, and quarters be x, y, and z, respectively

Then we get the following: "number of coins" equation: x + y + z = 131 

"Coin-comparison" equation: z = y + 10_____y - z = - 10

"Money-value" equation: .05x + .1y + .25z = 21.55

x + 2y + 5z = 431 -------- Multiplying by 20 to make all coefficients and constant, integers

This gives us: 

x +  y +  z =  131 ------- eq (i)

     y -  z = - 10 ------- eq (ii)

x + 2y + 5z =  431 ------- eq (iii)

We take the coefficients on the variables in each equation, along with their constants to get the following AUGMENTED matrix:

 

RELATED QUESTIONS

Mike has 19 coins (nickels, dimes, and quarters) in his piggy bank with a total value of... (answered by nyc_function,Fombitz)

A coin collection contains nickels, dimes, and quarters. There are twice as many dimes as  (answered by ikleyn)

A piggy bank contains nickels, dimes and quarters. There are three times as many dimes as  (answered by richwmiller)

There is a collection of nickels, dimes, and quarters with total value of $47.60. There... (answered by ikleyn,ewatrrr)

There is a collection of nickels, dimes, and quarters with total value of $47.60. There... (answered by CubeyThePenguin)

A jar contains nickels, dimes, and quarters. There are 105 coins with a total
value of... (answered by josmiceli)

You took $10 in quarters, dimes and nickels from a jar of spare change. If you have twice  (answered by josgarithmetic,MathTherapy,ikleyn)

you have 55 coins totaling $10.00. There are more nickels than pennies, more dimes than... (answered by ankor@dixie-net.com)

A collection of 35 coins consisting of dimes,nickels and quarters has a combined value of  (answered by lwsshak3)