Question

Devang has a collection of dimes and nickels that total $1.10. He has a total of 15 coins. Which matrix can be used to represent this system of linear equations to determine the number of dimes and nickels devang has ?

Answer 1

AX = b or
`\left[\begin{array}{cc}1&1\\0.1&0.05\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}15\\1.10\end{array}\right]`

The above matrix can be used to determine the number of dimes x and nickels y.

Explanation:

Here, total number of coins = 15

Let us assume the number of dimes = x

Also, let us assume the number of nickels = y

So, x + y = 15 .... (1)

Again, 1 dime = $0.1

So, x dimes = x ($0.1) = $ (0.1 x)

1 nickel = $0.05

So, y nickels = y ($0.05) = $ (0.05 y)

Also, total value of coins = $1.10

⇒ 0.1 x + 0.05 y = 1.10 .... (2)

So, from (1) and (2) the matrix can be written as:

AX = b or
`\left[\begin{array}{cc}1&1\\0.1&0.05\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}15\\1.10\end{array}\right]`

The above matrix can be used to determine the number of dimes x and nickels y.