Question

I have 12 coins in my pocket. They are all either dimes or nickels. The value of the coins is .85 how many of each coin do I have

Answer 1

To solve this problem, we will set and solve a system of equations.

Let x be the number of nickels you have in your pocket, and y the number of dimes, then with the given information, we can set the following system of equations:

`\begin{gathered} 0.05x+0.10y=0.85, \\ x+y=12. \end{gathered}`

Multiplying the second equation by -0.10 and adding it to the first equation, we get:

`0.05x-0.10x+0.10y-0.10y=0.85-1.2.`

Solving the above equation for x, we get:

`\begin{gathered} -0.05x=-0.35, \\ x=(-0.35)/(-0.05), \\ x=7. \end{gathered}`

Solving the second equation of the system for y, we get:

`y=12-x.`

Finally, substituting x=7, we get:

`y=12-7=5.`

Answer:

`\begin{gathered} 7\text{ nickels, } \\ 5\text{ dimes.} \end{gathered}`