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Answer: the answer is A
Step-by-step explanation:
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You can use variables to denote the amount of quarters and dimes Indira has got, and then form the equations.
The augmented matrix that can be used to determine the number of quarters and dimes in the collection is
[tex]\left[\begin{array}{ccc}1&1&18\\0.25&1&4.2\end{array}\right][/tex]
What is augmented matrix?
The word augment means to extend something to make it more rich.
When two matrices are jointly written as a single matrix, then that final matrix is called augmented matrix.
We usually use augmented matrix to do row and column operations faster to reach to the solution of considered system of equation.
Since it is given that she has got 18 coins worth $4.20 and only got quarters and dimes, thus, assuming that she has got [tex]x[/tex] quarters and [tex]y[/tex] dimes.
Since we know that
1 quarter = $0.25
1 dime = $0.1
Thus,
[tex]x \: \rm quarters = x \times 0.25 \: \rm dollars\\y \: dimes = y \times 0.1 \: \rm dollars[/tex]
As she has got 18 coins worth $4.20 thus,
[tex]x + y = 18\\0.25x + y = 4.20[/tex]
In matrix form, this system is written as
[tex]\left[\begin{array}{cc}1&1\\0.25&1\end{array}\right] . \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}18\\4.2\end{array}\right][/tex]
The when we augment the constant involving matrices, we get
[tex]\left[\begin{array}{ccc}1&1&18\\0.25&1&4.2\end{array}\right][/tex]
Thus,
The augmented matrix that can be used to determine the number of quarters and dimes in the collection is
[tex]\left[\begin{array}{ccc}1&1&18\\0.25&1&4.2\end{array}\right][/tex]
Learn more here about augmented matrix here:
https://brainly.com/question/15280480
