You have $3.80 in quarters and dimes. You have three fewer quarters than dimes. What would the associated system of equations look like in augmented matrix form?
Let's represent the number of quarters as "q" and the number of dimes as "d".
We know that you have 3 fewer quarters than dimes, so we can write the equation:
q = d - 3
We also know the total value of the quarters and dimes is $3.80. Since the value of a quarter is $0.25 and the value of a dime is $0.10, we can write the equation:
0.25q + 0.10d = 3.80
To represent this system of equations in augmented matrix form, we can set up the following matrix:
[ 1 -1 | -3 ]
[ 0.25 0.10 | 3.80 ]