You have $2.60 in quarters and dimes. You have five fewer quarters than dimes. What would the associated system of equations look like in augmented matrix form?
A |0.25 -5|2.6|
|0.1 5| 1 |
B |0.25 2.6| 1 |
| 1 5 | -1|
C |0.1 -1 |2.6|
|1 0.25| 5 |
D |0.1 0.25|2.6|***
| 1 -1 | 5 |
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D is correct
The correct answer is D:
| 0.1 0.25 | 2.6 |
| 1 -1 | 5 |
The correct answer would be D:
|0.1 0.25|2.6|
| 1 -1 | 5 |
To understand why, we need to set up the system of equations based on the information given. Let's represent the number of dimes with "x" and the number of quarters with "y".
From the problem, we know that the total value of the quarters and dimes is $2.60. Since the value of a quarter is $0.25 and the value of a dime is $0.10, we can write the first equation as:
0.25y + 0.10x = 2.60
We also know that there are five fewer quarters than dimes, which can be represented as:
y = x - 5
In matrix form, the augmented matrix would look like:
|0.1 0.25|2.6|
| 1 -1 | 5 |