# 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.? ##### 1 Answer May 1, 2018 $n = 4 + d$$n + 2 d = 25$$d = 7$#### Explanation: 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 $d$. First, we know that John has four more nickels than dimes. Let $n$be the number of nickels and $d$the number of dimes. Then $n = 4 + d$represents the relative amounts of nickels and dimes. Additionally, we know that our change totals $1.25. Since dimes are worth 10 cents and nickels worth 5, this can be modeled with the equation $0.05 n + 0.1 d = 1.25$. To eliminate the decimals, we can multiply this through by 20 to yield $n + 2 d = 25$.

We then have the two equations:
$n = 4 + d$
$n + 2 d = 25$

We will substitute the first into the second, giving
$n + 2 d = 25 \to \left(4 + d\right) + 2 d = 25 \to 3 d = 21 \to d = 7$.

This gives us our answer; we have $7$ dimes. (Plugging this value of $d$ into the first equation also reveals that we have $11$ nickels.)