John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, #d#, in his pocket.?
In this case, you would not write an equation, you would write two equations. This will give you a system with two equations and two unknowns. The equations will be linearly independent, meaning you'll be able to use them to solve for
First, we know that John has four more nickels than dimes. Let
Additionally, we know that our change totals
We then have the two equations:
We will substitute the first into the second, giving
This gives us our answer; we have