Question

A student has 10 coins in her pocket that have a value of $0.85. The coins are either

nickels or dimes. Which system of linear equations represents this scenario?

Answer 1

`\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.`

Explanation:

System of Equations

Let's call:

x = number of nickels in the student's pocket

y = number of dimes in the student's pocket

Each nickel has a value of $0.05, so x nickels have a value of 0.05x

Each dime has a value of $0.10, so y dimes have a value of 0.10y

The student has a total of 10 coins, thus:

`x+y=10`

The total value of the coins is $0.85, thus

`0.05x+0.10y=0.85`

The system of linear equations that represents this scenario is:

`\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.`