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expeople1 [14]
3 years ago
15

A man has 30 coins, which are all dimes or nickels. Their combined value is $2.10. How many coins of each kind does he have? Let

x = the number of nickels. Let y = the number of dimes. Which of the following matrices could be used to solve the problem
Mathematics
2 answers:
enyata [817]3 years ago
6 0

Answer:

The equation could be

\left[\begin{array}{ccc}1&1\\0.05&0.1\end{array}\right] \times \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}30\\2.10\end{array}\right]

Step-by-step explanation:

The equation to represent the number of coins would be

x + y = 30

The equation to represent the amount of money the coins are worth would be

0.05x + 0.10y = 2.10

This gives us the system

\left \{ {{x+y=30} \atop {0.05x+0.10y=2.10}} \right.

Using matrices, the first matrix will be the coefficient matrix.  This contains the coefficients for x and y for both equations:

\left[\begin{array}{ccc}1&1\\0.05&0.10\end{array}\right]

The second matrix will be the variable matrix, containing the variables for both equations:

\left[\begin{array}{ccc}x\\y\end{array}\right]

The matrix after the equals sign will be the constant matrix:

\left[\begin{array}{ccc}30\\2.10\end{array}\right]

This gives us the matrix equation above.

Yuliya22 [10]3 years ago
5 0

x + y = 30


5x + 10 y = 210


As a matrix equation that's


\begin{pmatrix} 1 & 1 \\ 5 & 10 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix}30\\ 210 \end{pmatrix}




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